Zabrodin, Anton V. On integrability of the deformed Ruijsenaars-Schneider system. (English. Russian original) Zbl 07771682 Russ. Math. Surv. 78, No. 2, 349-386 (2023); translation from Usp. Mat. Nauk 78, No. 2, 149-188 (2023). MSC: 37J35 37J70 37K10 33E05 PDFBibTeX XMLCite \textit{A. V. Zabrodin}, Russ. Math. Surv. 78, No. 2, 349--386 (2023; Zbl 07771682); translation from Usp. Mat. Nauk 78, No. 2, 149--188 (2023) Full Text: DOI arXiv MNR
Kozlov, Valery V. On the integrability of the equations of dynamics in a non-potential force field. (English. Russian original) Zbl 1526.37071 Russ. Math. Surv. 77, No. 6, 1087-1106 (2022); translation from Usp. Mat. Nauk 77, No. 6, 137-158 (2022). MSC: 37J35 70H06 70H33 PDFBibTeX XMLCite \textit{V. V. Kozlov}, Russ. Math. Surv. 77, No. 6, 1087--1106 (2022; Zbl 1526.37071); translation from Usp. Mat. Nauk 77, No. 6, 137--158 (2022) Full Text: DOI MNR
Grinevich, Petr G.; Santini, Paolo M. The finite-gap method and the periodic Cauchy problem for \((2+1)\)-dimensional anomalous waves for the focusing Davey-Stewartson 2 equation. (English. Russian original) Zbl 1522.35465 Russ. Math. Surv. 77, No. 6, 1029-1059 (2022); translation from Usp. Mat. Nauk 77, No. 6, 77-108 (2022). MSC: 35Q55 35Q41 35C08 35C20 35B40 35B20 37K10 37K15 37K20 PDFBibTeX XMLCite \textit{P. G. Grinevich} and \textit{P. M. Santini}, Russ. Math. Surv. 77, No. 6, 1029--1059 (2022; Zbl 1522.35465); translation from Usp. Mat. Nauk 77, No. 6, 77--108 (2022) Full Text: DOI arXiv MNR
Buchstaber, Victor M.; Mikhailov, Alexander V. Integrable polynomial Hamiltonian systems and symmetric powers of plane algebraic curves. (English. Russian original) Zbl 1484.14072 Russ. Math. Surv. 76, No. 4, 587-652 (2021); translation from Usp. Mat. Nauk 76, No. 4, 37-104 (2021). Reviewer: Ahmed Lesfari (El Jadida) MSC: 14H70 14K25 37J35 PDFBibTeX XMLCite \textit{V. M. Buchstaber} and \textit{A. V. Mikhailov}, Russ. Math. Surv. 76, No. 4, 587--652 (2021; Zbl 1484.14072); translation from Usp. Mat. Nauk 76, No. 4, 37--104 (2021) Full Text: DOI
Bolsinov, Aleksei V.; Veselov, Aleksandr P.; Ye, Yiru Chaos and integrability in \(\operatorname{SL}(2,\mathbb{R})\)-geometry. (English. Russian original) Zbl 1496.37031 Russ. Math. Surv. 76, No. 4, 557-586 (2021); translation from Usp. Mat. Nauk 76, No. 4, 3-36 (2021). MSC: 37D40 37J35 37J39 57M50 57K10 PDFBibTeX XMLCite \textit{A. V. Bolsinov} et al., Russ. Math. Surv. 76, No. 4, 557--586 (2021; Zbl 1496.37031); translation from Usp. Mat. Nauk 76, No. 4, 3--36 (2021) Full Text: DOI arXiv
Sokolov, Vladimir V. Non-Abelian \(\mathfrak{so}_3\) Euler top. (English. Russian original) Zbl 1477.34034 Russ. Math. Surv. 76, No. 1, 183-185 (2021); translation from Usp. Mat. Nauk 76, No. 1, 195-196 (2021). MSC: 34A34 34C14 34A05 37J35 70H06 PDFBibTeX XMLCite \textit{V. V. Sokolov}, Russ. Math. Surv. 76, No. 1, 183--185 (2021; Zbl 1477.34034); translation from Usp. Mat. Nauk 76, No. 1, 195--196 (2021) Full Text: DOI arXiv
Kozlov, Valeriĭ V. Quadratic conservation laws for equations of mathematical physics. (English. Russian original) Zbl 1489.34087 Russ. Math. Surv. 75, No. 3, 445-494 (2020); translation from Usp. Mat. Nauk 75, No. 3, 55-106 (2020). Reviewer: Ti-Jun Xiao (Fudan) MSC: 34G10 37J35 PDFBibTeX XMLCite \textit{V. V. Kozlov}, Russ. Math. Surv. 75, No. 3, 445--494 (2020; Zbl 1489.34087); translation from Usp. Mat. Nauk 75, No. 3, 55--106 (2020) Full Text: DOI
Kozlov, V. V. Linear systems with quadratic integral and complete integrability of the Schrödinger equation. (English. Russian original) Zbl 1442.37079 Russ. Math. Surv. 74, No. 5, 959-961 (2019); translation from Usp. Mat. Nauk 74, No. 5, 189-190 (2019). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 37K10 35Q55 35L05 PDFBibTeX XMLCite \textit{V. V. Kozlov}, Russ. Math. Surv. 74, No. 5, 959--961 (2019; Zbl 1442.37079); translation from Usp. Mat. Nauk 74, No. 5, 189--190 (2019) Full Text: DOI
Buchstaber, V. M.; Veselov, A. P. Conway topograph, \(\operatorname{PGL}_2(\mathbb{Z})\)-dynamics and two-valued groups. (English. Russian original) Zbl 1484.11153 Russ. Math. Surv. 74, No. 3, 387-430 (2019); translation from Usp. Mat. Nauk 74, No. 3, 17-62 (2019). Reviewer: Tathagata Basak (Ames) MSC: 11H55 20N20 37P99 PDFBibTeX XMLCite \textit{V. M. Buchstaber} and \textit{A. P. Veselov}, Russ. Math. Surv. 74, No. 3, 387--430 (2019; Zbl 1484.11153); translation from Usp. Mat. Nauk 74, No. 3, 17--62 (2019) Full Text: DOI
Mokhov, O. I.; Strizhova, N. A. Liouville integrability of the reduction of the associativity equations on the set of stationary points of an integral in the case of three primary fields. (English. Russian original) Zbl 1439.37069 Russ. Math. Surv. 74, No. 2, 369-371 (2019); translation from Usp. Mat. Nauk 74, No. 2,191-192 (2019). MSC: 37K10 37K20 37K30 PDFBibTeX XMLCite \textit{O. I. Mokhov} and \textit{N. A. Strizhova}, Russ. Math. Surv. 74, No. 2, 369--371 (2019; Zbl 1439.37069); translation from Usp. Mat. Nauk 74, No. 2,191--192 (2019) Full Text: DOI
Bychkov, B. S.; Mikhailov, A. V. Polynomial graph invariants and linear hierarchies. (English. Russian original) Zbl 1439.37070 Russ. Math. Surv. 74, No. 2, 366-368 (2019); translation from Usp. Mat. Nauk 74, No. 2, 189-190 (2019). Reviewer: Ahmed Lesfari (El Jadida) MSC: 37K20 37K25 37K30 37K10 05C31 PDFBibTeX XMLCite \textit{B. S. Bychkov} and \textit{A. V. Mikhailov}, Russ. Math. Surv. 74, No. 2, 366--368 (2019; Zbl 1439.37070); translation from Usp. Mat. Nauk 74, No. 2, 189--190 (2019) Full Text: DOI
Kordyukov, Yu. A.; Taimanov, I. A. Trace formula for the magnetic Laplacian. (English. Russian original) Zbl 1433.58019 Russ. Math. Surv. 74, No. 2, 325-361 (2019); translation from Usp. Mat. Nauk 74, No. 2, 149-186 (2019). Reviewer: Vicenţiu D. Rădulescu (Craiova) MSC: 58J05 58J50 37J35 58J37 81Q20 PDFBibTeX XMLCite \textit{Yu. A. Kordyukov} and \textit{I. A. Taimanov}, Russ. Math. Surv. 74, No. 2, 325--361 (2019; Zbl 1433.58019); translation from Usp. Mat. Nauk 74, No. 2, 149--186 (2019) Full Text: DOI arXiv
Grinevich, P. G.; Santini, P. M. The finite-gap method and the periodic NLS Cauchy problem of anomalous waves for a finite number of unstable modes. (English. Russian original) Zbl 1454.35340 Russ. Math. Surv. 74, No. 2, 211-263 (2019); translation from Usp. Mat. Nauk 74, No. 2, 27-80 (2019). MSC: 35Q55 37K10 35C08 74J30 78A60 76B25 76B15 PDFBibTeX XMLCite \textit{P. G. Grinevich} and \textit{P. M. Santini}, Russ. Math. Surv. 74, No. 2, 211--263 (2019; Zbl 1454.35340); translation from Usp. Mat. Nauk 74, No. 2, 27--80 (2019) Full Text: DOI arXiv
Bialy, M.; Mironov, A. E. Polynomial non-integrability of magnetic billiards on the sphere and the hyperbolic plane. (English. Russian original) Zbl 1439.37054 Russ. Math. Surv. 74, No. 2, 187-209 (2019); translation from Usp. Mat. Nauk 74, No. 2, 3-26 (2019). MSC: 37J30 37J35 37J38 37C83 PDFBibTeX XMLCite \textit{M. Bialy} and \textit{A. E. Mironov}, Russ. Math. Surv. 74, No. 2, 187--209 (2019; Zbl 1439.37054); translation from Usp. Mat. Nauk 74, No. 2, 3--26 (2019) Full Text: DOI arXiv
Mal’tsev, A. Ya.; Novikov, S. P. Topological integrability, classical and quantum chaos, and the theory of dynamical systems in the physics of condensed matter. (English. Russian original) Zbl 1439.37062 Russ. Math. Surv. 74, No. 1, 141-173 (2019); translation from Usp. Mat. Nauk 74, No. 1, 149-184 (2019). Reviewer: William J. Satzer Jr. (St. Paul) MSC: 37J39 37J35 37J30 37C55 81Q50 37N15 82C70 PDFBibTeX XMLCite \textit{A. Ya. Mal'tsev} and \textit{S. P. Novikov}, Russ. Math. Surv. 74, No. 1, 141--173 (2019; Zbl 1439.37062); translation from Usp. Mat. Nauk 74, No. 1, 149--184 (2019) Full Text: DOI arXiv
Kozlov, V. V. Tensor invariants and integration of differential equations. (English. Russian original) Zbl 1439.37057 Russ. Math. Surv. 74, No. 1, 111-140 (2019); translation from Usp. Mat. Nauk 74, No. 1, 117-148 (2019). MSC: 37J35 37J06 37J39 70E40 PDFBibTeX XMLCite \textit{V. V. Kozlov}, Russ. Math. Surv. 74, No. 1, 111--140 (2019; Zbl 1439.37057); translation from Usp. Mat. Nauk 74, No. 1, 117--148 (2019) Full Text: DOI
Buchstaber, Viktor M.; Mikhailov, Aleksandr V. Polynomial Hamiltonian integrable systems on symmetric powers of plane curves. (English. Russian original) Zbl 1419.14053 Russ. Math. Surv. 73, No. 6, 1122-1124 (2018); translation from Usp. Mat. Nauk 73, No. 6, 193-194 (2018). Reviewer: Ahmed Lesfari (El Jadida) MSC: 14H70 37J05 37J35 PDFBibTeX XMLCite \textit{V. M. Buchstaber} and \textit{A. V. Mikhailov}, Russ. Math. Surv. 73, No. 6, 1122--1124 (2018; Zbl 1419.14053); translation from Usp. Mat. Nauk 73, No. 6, 193--194 (2018) Full Text: DOI
Mokhov, Oleg I.; Strizhova, Nadezhda A. Classification of the associativity equations possessing a Hamiltonian structure of Dubrovin-Novikov type. (English. Russian original) Zbl 1393.37071 Russ. Math. Surv. 73, No. 1, 175-177 (2018); translation from Usp. Mat. Nauk 73, No. 1, 183-184 (2018). MSC: 37K05 37K10 53D45 53B20 PDFBibTeX XMLCite \textit{O. I. Mokhov} and \textit{N. A. Strizhova}, Russ. Math. Surv. 73, No. 1, 175--177 (2018; Zbl 1393.37071); translation from Usp. Mat. Nauk 73, No. 1, 183--184 (2018) Full Text: DOI
Takhtajan, Leon A.; Alekseev, Anton Yu.; Aref’eva, Irina Ya.; Semenov-Tian-Shansky, Michael A.; Sklyanin, Evgeny K.; Smirnov, Fedor A.; Shatashvili, Samson L. Scientific heritage of L. D. Faddeev. Survey of papers. (English. Russian original) Zbl 1396.81008 Russ. Math. Surv. 72, No. 6, 977-1081 (2017); translation from Usp. Mat. Nauk 72, No. 6, xx (2017). MSC: 81-03 01A60 01A70 16T25 17B37 35J10 35P25 35Q53 35Q55 37K15 58B32 58J52 70S15 81R50 81S40 81T10 81T13 81T50 81T70 81U40 82B23 82C23 PDFBibTeX XMLCite \textit{L. A. Takhtajan} et al., Russ. Math. Surv. 72, No. 6, 977--1081 (2017; Zbl 1396.81008); translation from Usp. Mat. Nauk 72, No. 6, xx (2017) Full Text: DOI
Mokhov, Oleg I. Pencils of compatible metrics and integrable systems. (English. Russian original) Zbl 1394.37101 Russ. Math. Surv. 72, No. 5, 889-937 (2017); translation from Usp. Mat. Nauk 72, No. 5, 113-164 (2017). Reviewer: Dumitru Motreanu (Juiz de Fora) MSC: 37K05 37K10 37K25 53B21 53C21 53B50 PDFBibTeX XMLCite \textit{O. I. Mokhov}, Russ. Math. Surv. 72, No. 5, 889--937 (2017; Zbl 1394.37101); translation from Usp. Mat. Nauk 72, No. 5, 113--164 (2017) Full Text: DOI
Buryak, Alexandr Y. New approaches to integrable hierarchies of topological type. (English. Russian original) Zbl 1400.14073 Russ. Math. Surv. 72, No. 5, 841-887 (2017); translation from Usp. Mat. Nauk 72, No. 5, 63-112 (2017). Reviewer: Vladislav Nikolaevich Dumachev (Voronezh) MSC: 14H10 37K10 14N35 PDFBibTeX XMLCite \textit{A. Y. Buryak}, Russ. Math. Surv. 72, No. 5, 841--887 (2017; Zbl 1400.14073); translation from Usp. Mat. Nauk 72, No. 5, 63--112 (2017) Full Text: DOI
Bolotin, S. V.; Kozlov, V. V. Topological approach to the generalized \(n\)-centre problem. (English. Russian original) Zbl 1427.70031 Russ. Math. Surv. 72, No. 3, 451-478 (2017); translation from Usp. Mat. Nauk 72, No. 3, 65-96 (2017). MSC: 70F10 37N05 70G40 PDFBibTeX XMLCite \textit{S. V. Bolotin} and \textit{V. V. Kozlov}, Russ. Math. Surv. 72, No. 3, 451--478 (2017; Zbl 1427.70031); translation from Usp. Mat. Nauk 72, No. 3, 65--96 (2017) Full Text: DOI arXiv
Grinevich, P. G.; Novikov, S. P. On \(s\)-meromorphic ordinary differential operators. (English) Zbl 1418.34159 Russ. Math. Surv. 71, No. 6, 1143-1145 (2016); translation from Usp. Mat. Nauk 71, No. 6, 161-162 (2016). MSC: 34L40 34L05 34M05 37K10 37K15 PDFBibTeX XMLCite \textit{P. G. Grinevich} and \textit{S. P. Novikov}, Russ. Math. Surv. 71, No. 6, 1143--1145 (2016; Zbl 1418.34159); translation from Usp. Mat. Nauk 71, No. 6, 161--162 (2016) Full Text: DOI
Kozlov, V. V. Polynomial conservation laws for the Lorentz gas and the Boltzmann-Gibbs gas. (English. Russian original) Zbl 1418.37090 Russ. Math. Surv. 71, No. 2, 253-290 (2016); translation from Usp. Mat. Nauk 71, No. 2, 81-120 (2016). MSC: 37J05 37A60 37J30 82D05 37D50 70F35 70H33 70H08 PDFBibTeX XMLCite \textit{V. V. Kozlov}, Russ. Math. Surv. 71, No. 2, 253--290 (2016; Zbl 1418.37090); translation from Usp. Mat. Nauk 71, No. 2, 81--120 (2016) Full Text: DOI
Dynnikov, I. A. On a new discretization of complex analysis. (English. Russian original) Zbl 1353.39004 Russ. Math. Surv. 70, No. 6, 1031-1050 (2015); translation from Usp. Mat. Nauk 70, No. 6, 63-84 (2015). Reviewer: Miloš Čanak (Beograd) MSC: 39A12 39A45 37J35 PDFBibTeX XMLCite \textit{I. A. Dynnikov}, Russ. Math. Surv. 70, No. 6, 1031--1050 (2015; Zbl 1353.39004); translation from Usp. Mat. Nauk 70, No. 6, 63--84 (2015) Full Text: DOI
Bolotin, S. V.; Treschev, D. V. The anti-integrable limit. (English. Russian original) Zbl 1361.37056 Russ. Math. Surv. 70, No. 6, 975-1030 (2015); translation from Usp. Mat. Nauk 70, No. 6, 3-62 (2015). MSC: 37J30 37J15 37B40 PDFBibTeX XMLCite \textit{S. V. Bolotin} and \textit{D. V. Treschev}, Russ. Math. Surv. 70, No. 6, 975--1030 (2015; Zbl 1361.37056); translation from Usp. Mat. Nauk 70, No. 6, 3--62 (2015) Full Text: DOI
Grinevich, P. G.; Mironov, A. E.; Novikov, S. P. On the non-relativistic two-dimensional purely magnetic supersymmetric Pauli operator. (English. Russian original) Zbl 1330.81080 Russ. Math. Surv. 70, No. 2, 299-329 (2015); translation from Usp. Mat. Nauk 70, No. 2, 109-140 (2015). Reviewer: Michael Perelmuter (Kyïv) MSC: 81Q05 35C05 35J10 35J67 37K10 35C08 PDFBibTeX XMLCite \textit{P. G. Grinevich} et al., Russ. Math. Surv. 70, No. 2, 299--329 (2015; Zbl 1330.81080); translation from Usp. Mat. Nauk 70, No. 2, 109--140 (2015) Full Text: DOI arXiv
Dragović, V. I.; Radnović, M. Pseudo-integrable billiards and double reflection nets. (English. Russian original) Zbl 1358.37070 Russ. Math. Surv. 70, No. 1, 1-31 (2015); translation from Usp. Mat. Nauk. 70, No. 1, 3-34 (2015). MSC: 37D50 37J35 39A12 PDFBibTeX XMLCite \textit{V. I. Dragović} and \textit{M. Radnović}, Russ. Math. Surv. 70, No. 1, 1--31 (2015; Zbl 1358.37070); translation from Usp. Mat. Nauk. 70, No. 1, 3--34 (2015) Full Text: DOI
Grinevich, P. G.; Novikov, S. P. Discrete \(SL_{n}\)-connections and self-adjoint difference operators on 2-dimensional manifolds. (English. Russian original) Zbl 1282.39006 Russ. Math. Surv. 68, No. 5, 861-887 (2013); translation from Usp. Mat. Nauk 68, No. 5, 81-110 (2013). MSC: 39A12 37J35 39A70 47B39 44A10 PDFBibTeX XMLCite \textit{P. G. Grinevich} and \textit{S. P. Novikov}, Russ. Math. Surv. 68, No. 5, 861--887 (2013; Zbl 1282.39006); translation from Usp. Mat. Nauk 68, No. 5, 81--110 (2013) Full Text: DOI arXiv
Gontsov, R. R.; Poberezhnyi, V. A.; Helminck, G. F. On deformations of linear differential systems. (English. Russian original) Zbl 1230.34080 Russ. Math. Surv. 66, No. 1, 63-105 (2011); translation from Usp. Mat. Nauk. 66, No. 1, 65-110 (2011). Reviewer: Andrei A. Kapaev (Trieste) MSC: 34M35 34A26 34M56 53C07 32G34 PDFBibTeX XMLCite \textit{R. R. Gontsov} et al., Russ. Math. Surv. 66, No. 1, 63--105 (2011; Zbl 1230.34080); translation from Usp. Mat. Nauk. 66, No. 1, 65--110 (2011) Full Text: DOI
Grinevich, P. G.; Mironov, A. E.; Novikov, S. P. 2D-Schrödinger operator, \((2+1)\) evolution systems and new reductions, 2D-Burgers hierarchy and inverse problem data. (English. Russian original) Zbl 1231.35199 Russ. Math. Surv. 65, No. 3, 580-582 (2010); translation from Uspekhi Mat. Nauk. 65, No. 3, 195-196 (2010). Reviewer: Dmitry Shepelsky (Kharkov) MSC: 35Q53 37K10 35R30 PDFBibTeX XMLCite \textit{P. G. Grinevich} et al., Russ. Math. Surv. 65, No. 3, 580--582 (2010; Zbl 1231.35199); translation from Uspekhi Mat. Nauk. 65, No. 3, 195--196 (2010) Full Text: DOI
Mokhov, O. I. Riemann invariants of semisimple non-locally bi-Hamiltonian systems of hydrodynamic type and compatible metrics. (English. Russian original) Zbl 1218.37092 Russ. Math. Surv. 65, No. 6, 1183-1185 (2010). Reviewer: Vladislav Nikolaevich Dumachev (Voronezh) MSC: 37K10 37K25 53B20 70G45 PDFBibTeX XMLCite \textit{O. I. Mokhov}, Russ. Math. Surv. 65, No. 6, 1183--1185 (2010; Zbl 1218.37092) Full Text: DOI
Dragović, V.; Radnović, M. Integrable billiards and quadrics. (English. Russian original) Zbl 1202.37078 Russ. Math. Surv. 65, No. 2, 319-379 (2010); translation from Usp. Mat. Nauk 65, No. 2, 133-194 (2010). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 37J35 58E07 70H06 PDFBibTeX XMLCite \textit{V. Dragović} and \textit{M. Radnović}, Russ. Math. Surv. 65, No. 2, 319--379 (2010; Zbl 1202.37078); translation from Usp. Mat. Nauk 65, No. 2, 133--194 (2010) Full Text: DOI
Bolsinov, A. V.; Borisov, A. V.; Mamaev, I. S. Topology and stability of integrable systems. (English. Russian original) Zbl 1202.37077 Russ. Math. Surv. 65, No. 2, 259-317 (2010); translation from Usp. Mat. Nauk 65, No. 2, 71-132 (2010). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 37J35 37-02 37J05 37J20 37J25 70E40 70E50 70G40 70H14 PDFBibTeX XMLCite \textit{A. V. Bolsinov} et al., Russ. Math. Surv. 65, No. 2, 259--317 (2010; Zbl 1202.37077); translation from Usp. Mat. Nauk 65, No. 2, 71--132 (2010) Full Text: DOI
Soloviev, F. L. On the Hamiltonian form of equations of the elliptic spin Ruijsenaars-Schneider model. (English. Russian original) Zbl 1196.37098 Russ. Math. Surv. 64, No. 6, 1142-1144 (2009); translation from Usp. Mat. Nauk 64, No. 6, 179-180 (2009). Reviewer: Ioan Bucataru (Iaşi) MSC: 37J35 34L40 35Q53 35Q55 PDFBibTeX XMLCite \textit{F. L. Soloviev}, Russ. Math. Surv. 64, No. 6, 1142--1144 (2009; Zbl 1196.37098); translation from Usp. Mat. Nauk 64, No. 6, 179--180 (2009) Full Text: DOI
Mokhov, O. I. On consistency of determinants on cubic lattices. (English. Russian original) Zbl 1176.39001 Russ. Math. Surv. 63, No. 6, 1146-1148 (2008); translation from Usp. Mat. Nauk 63, No. 6, 169-170 (2008). MSC: 39A05 15A15 37K10 11H06 52C05 PDFBibTeX XMLCite \textit{O. I. Mokhov}, Russ. Math. Surv. 63, No. 6, 1146--1148 (2008; Zbl 1176.39001); translation from Usp. Mat. Nauk 63, No. 6, 169--170 (2008) Full Text: DOI arXiv
Krichever, I. M. Abelian solutions of the soliton equations and Riemann-Schottky problems. (English. Russian original) Zbl 1164.37021 Russ. Math. Surv. 63, No. 6, 1011-1022 (2008); translation from Usp. Mat. Nauk 63, No. 6, 19-30 (2008). Reviewer: Iskander A. Taimanov (Novosibirsk) MSC: 37K20 14H40 14H42 35Q53 37K10 PDFBibTeX XMLCite \textit{I. M. Krichever}, Russ. Math. Surv. 63, No. 6, 1011--1022 (2008; Zbl 1164.37021); translation from Usp. Mat. Nauk 63, No. 6, 19--30 (2008) Full Text: DOI
Dubrovin, B. A. Hamiltonian PDEs and Frobenius manifolds. (English. Russian original) Zbl 1170.53072 Russ. Math. Surv. 63, No. 6, 999-1010 (2008); translation from Usp. Mat. Nauk 63, No. 6, 7-18 (2008). Reviewer: Sergiy Koshkin (Houston) MSC: 53D45 37K10 PDFBibTeX XMLCite \textit{B. A. Dubrovin}, Russ. Math. Surv. 63, No. 6, 999--1010 (2008; Zbl 1170.53072); translation from Usp. Mat. Nauk 63, No. 6, 7--18 (2008) Full Text: DOI
Golovko, V. A. Variational Schouten and Nijenhuis brackets. (English. Russian original) Zbl 1185.37147 Russ. Math. Surv. 63, No. 2, 360-362 (2008); translation from Usp. Mat. Nauk. 63, No. 2, 165-166 (2008). Reviewer: Radu Precup (Cluj-Napoca) MSC: 37K05 37K10 PDFBibTeX XMLCite \textit{V. A. Golovko}, Russ. Math. Surv. 63, No. 2, 360--362 (2008; Zbl 1185.37147); translation from Usp. Mat. Nauk. 63, No. 2, 165--166 (2008) Full Text: DOI
Komlov, A. V. Estimates of the Gevrey classes of scattering data for polynomial potentials. (English. Russian original) Zbl 1177.35179 Russ. Math. Surv. 63, No. 4, 788-789 (2008); translation from Usp. Mat. Nauk 63, No. 4, 189-190 (2008). MSC: 35Q51 37K10 37K30 PDFBibTeX XMLCite \textit{A. V. Komlov}, Russ. Math. Surv. 63, No. 4, 788--789 (2008; Zbl 1177.35179); translation from Usp. Mat. Nauk 63, No. 4, 189--190 (2008) Full Text: DOI
Domrin, A. V.; Domrina, A. V. On the divergence of the Kontsevich-Witten series. (English. Russian original) Zbl 1179.37091 Russ. Math. Surv. 63, No. 4, 773-775 (2008); translation from Usp. Mat. Nauk 63, No. 4, 185-186 (2008). Reviewer: Vjacheslav Yurko (Saratov) MSC: 37K15 35P25 37K10 PDFBibTeX XMLCite \textit{A. V. Domrin} and \textit{A. V. Domrina}, Russ. Math. Surv. 63, No. 4, 773--775 (2008; Zbl 1179.37091); translation from Usp. Mat. Nauk 63, No. 4, 185--186 (2008) Full Text: DOI
Penskoǐ, A. V. The Volterra system and the topology of the isospectral variety of zero-diagonal Jacobi matrices. (English. Russian original) Zbl 1155.58306 Russ. Math. Surv. 62, No. 3, 626-628 (2007); translation from Usp. Mat. Nauk 62, No. 3, 213-214 (2007). MSC: 58J53 37J35 47B36 37K10 15A30 57N15 PDFBibTeX XMLCite \textit{A. V. Penskoǐ}, Russ. Math. Surv. 62, No. 3, 626--628 (2007; Zbl 1155.58306); translation from Usp. Mat. Nauk 62, No. 3, 213--214 (2007) Full Text: DOI arXiv
Shamolin, M. V. A case of complete integrability in the dynamics on the tangent bundle of a two-dimensional sphere. (English. Russian original) Zbl 1137.37325 Russ. Math. Surv. 62, No. 5, 1009-1011 (2007); translation from Usp. Mat. Nauk 62, No. 5, 169-170 (2007). MSC: 37J35 70E15 70E40 34C40 PDFBibTeX XMLCite \textit{M. V. Shamolin}, Russ. Math. Surv. 62, No. 5, 1009--1011 (2007; Zbl 1137.37325); translation from Usp. Mat. Nauk 62, No. 5, 169--170 (2007) Full Text: DOI
Grinevich, P. G.; Novikov, R. G. The Cauchy kernel for the Novikov-Dynnikov DN-discrete complex analysis in triangular lattices. (English. Russian original) Zbl 1141.39019 Russ. Math. Surv. 62, No. 4, 799-801 (2007); translation from Usp. Mat. Nauk 62, No. 4, 155-156 (2007). MSC: 39A12 30E20 35E05 35C15 37K10 39A70 PDFBibTeX XMLCite \textit{P. G. Grinevich} and \textit{R. G. Novikov}, Russ. Math. Surv. 62, No. 4, 799--801 (2007; Zbl 1141.39019); translation from Usp. Mat. Nauk 62, No. 4, 155--156 (2007) Full Text: DOI
Bukhshtaber, V. M.; Leĭkin, D. V. Functional equations defining multiplication in a continuous Krichever-Novikov basis. (English) Zbl 1152.47302 Russ. Math. Surv. 61, No. 1, 165-167 (2006); translation from Usp. Mat. Nauk 61, No. 1, 171-172 (2005). Reviewer: Khalil Ezzinbi (Marrakech) MSC: 37K10 14H70 30D45 35Q58 37K20 39B32 PDFBibTeX XMLCite \textit{V. M. Bukhshtaber} and \textit{D. V. Leĭkin}, Russ. Math. Surv. 61, No. 1, 165--167 (2006; Zbl 1152.47302); translation from Usp. Mat. Nauk 61, No. 1, 171--172 (2005) Full Text: DOI MNR
Bukhshtaber, V. M.; Krichever, I. M. Integrable equations, addition theorems, and the Riemann-Schottky problem. (English) Zbl 1134.14306 Russ. Math. Surv. 61, No. 1, 19-78 (2006); translation from Usp. Mat. Nauk 61, No. 1, 25-84 (2006). MSC: 14H42 14H70 37K10 37K20 PDFBibTeX XMLCite \textit{V. M. Bukhshtaber} and \textit{I. M. Krichever}, Russ. Math. Surv. 61, No. 1, 19--78 (2006; Zbl 1134.14306); translation from Usp. Mat. Nauk 61, No. 1, 25--84 (2006) Full Text: DOI
Mokhov, O. I. Systems of integrals in involution and the associativity equations. (English. Russian original) Zbl 1132.37025 Russ. Math. Surv. 61, No. 3, 568-570 (2006); translation from Usp. Mat. Nauk 61, No. 3, 175-176 (2006). Reviewer: Luen-Chau Li (University Park) MSC: 37K10 37K05 53D45 81R12 PDFBibTeX XMLCite \textit{O. I. Mokhov}, Russ. Math. Surv. 61, No. 3, 568--570 (2006; Zbl 1132.37025); translation from Usp. Mat. Nauk 61, No. 3, 175--176 (2006) Full Text: DOI
Mokhov, O. I. Classification of multidimensional Poisson brackets of hydrodynamic type. (English. Russian original) Zbl 1123.37029 Russ. Math. Surv. 61, No. 2, 356-358 (2006); translation from Usp. Mat. Nauk 61, No. 2, 167-168 (2006). Reviewer: Jan Chrastina (Brno) MSC: 37K05 37K10 35Q53 37N10 37K25 PDFBibTeX XMLCite \textit{O. I. Mokhov}, Russ. Math. Surv. 61, No. 2, 356--358 (2006; Zbl 1123.37029); translation from Usp. Mat. Nauk 61, No. 2, 167--168 (2006) Full Text: DOI
Shamolin, M. V. An integrable case of dynamical equations on \(\text{so}(4)\times\mathbb R^4\). (English) Zbl 1183.70019 Russ. Math. Surv. 60, No. 6, 1245-1246 (2005); translation from Usp. Mat. Nauk 60, No. 6, 233-234 (2005). MSC: 70E40 37J35 70H06 PDFBibTeX XMLCite \textit{M. V. Shamolin}, Russ. Math. Surv. 60, No. 6, 1245--1246 (2005; Zbl 1183.70019); translation from Usp. Mat. Nauk 60, No. 6, 233--234 (2005) Full Text: DOI
Marikhin, V. G.; Sokolov, V. V. On quasi-Stäckel Hamiltonians. (English) Zbl 1140.37017 Russ. Math. Surv. 60, No. 5, 981-983 (2005); translation from Usp. Mat. Nauk 60, No. 5, 175-176 (2005). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 37J35 70H05 PDFBibTeX XMLCite \textit{V. G. Marikhin} and \textit{V. V. Sokolov}, Russ. Math. Surv. 60, No. 5, 981--983 (2005; Zbl 1140.37017); translation from Usp. Mat. Nauk 60, No. 5, 175--176 (2005) Full Text: DOI
Ziglin, S. L. Integrability by quadratures of variational equations in systems with an additional first integral. (English) Zbl 1146.37037 Russ. Math. Surv. 60, No. 4, 802-803 (2005); translation from Usp. Mat. Nauk 60, No. 4, 213-214 (2005). Reviewer: Alois Klíč (Praha) MSC: 37J30 34M05 37F10 PDFBibTeX XMLCite \textit{S. L. Ziglin}, Russ. Math. Surv. 60, No. 4, 802--803 (2005; Zbl 1146.37037); translation from Usp. Mat. Nauk 60, No. 4, 213--214 (2005) Full Text: DOI
Sheinman, O. K. Highest-weight representations of Krichever-Novikov algebras and integrable systems. (English. Russian original) Zbl 1082.17012 Russ. Math. Surv. 60, No. 2, 370-372 (2005); translation from Usp. Mat. Nauk 60, No. 2, 177-178 (2005). Reviewer: Volodymyr Mazorchuk (Uppsala) MSC: 17B67 17B10 37K10 37K30 17B80 22E65 PDFBibTeX XMLCite \textit{O. K. Sheinman}, Russ. Math. Surv. 60, No. 2, 370--372 (2005; Zbl 1082.17012); translation from Usp. Mat. Nauk 60, No. 2, 177--178 (2005) Full Text: DOI
Bukhshtaber, V. M.; Lejkin, D. V. Trilinear functional equations. (English. Russian original) Zbl 1093.14049 Russ. Math. Surv. 60, No. 2, 341-343 (2005); translation from Usp. Mat. Nauk 60, No. 2, 151-152 (2005). Reviewer: V. V. Chueshev (Kemerovo) MSC: 14H70 14H40 33C20 37K10 PDFBibTeX XMLCite \textit{V. M. Bukhshtaber} and \textit{D. V. Lejkin}, Russ. Math. Surv. 60, No. 2, 341--343 (2005; Zbl 1093.14049); translation from Usp. Mat. Nauk 60, No. 2, 151--152 (2005) Full Text: DOI
Dynnikov, I. A.; Novikov, S. P. Topology of quasiperiodic functions on the plane. (English. Russian original) Zbl 1148.37043 Russ. Math. Surv. 60, No. 1, 1-26 (2005); translation from Usp. Mat. Nauk 60, No. 1, 3-28 (2005). MSC: 37N20 35B15 35L70 35Q53 37K10 82D35 PDFBibTeX XMLCite \textit{I. A. Dynnikov} and \textit{S. P. Novikov}, Russ. Math. Surv. 60, No. 1, 1--26 (2005; Zbl 1148.37043); translation from Usp. Mat. Nauk 60, No. 1, 3--28 (2005) Full Text: DOI arXiv
Mironov, A. E. Spectral subvarieties of a principally polarized abelian variety. (English. Russian original) Zbl 1071.14516 Russ. Math. Surv. 59, No. 5, 969-970 (2004); translation from Usp. Mat. Nauk 59, No. 5, 157-158 (2004). MSC: 14K12 14K25 37K10 PDFBibTeX XMLCite \textit{A. E. Mironov}, Russ. Math. Surv. 59, No. 5, 969--970 (2004; Zbl 1071.14516); translation from Usp. Mat. Nauk 59, No. 5, 157--158 (2004) Full Text: DOI
Mal’tsev, A. Ya. Averaging of weakly nonlocal symplectic structures. (English. Russian original) Zbl 1054.37040 Russ. Math. Surv. 59, No. 2, 389-390 (2004); translation from Usp. Mat. Nauk 59, No. 2, 193-194 (2004). MSC: 37K05 37K10 37N10 PDFBibTeX XMLCite \textit{A. Ya. Mal'tsev}, Russ. Math. Surv. 59, No. 2, 389--390 (2003; Zbl 1054.37040); translation from Usp. Mat. Nauk 59, No. 2, 193--194 (2004) Full Text: DOI arXiv
Mokhov, O. I. Nonlocal Hamiltonian operators of hydrodynamic type with flat metrics, and associativity equations. (English. Russian original) Zbl 1054.37042 Russ. Math. Surv. 59, No. 1, 191-192 (2004); translation from Usp. Mat. Nauk 59, No. 1, 187-188 (2004). MSC: 37K10 37K05 37K25 PDFBibTeX XMLCite \textit{O. I. Mokhov}, Russ. Math. Surv. 59, No. 1, 191--192 (2003; Zbl 1054.37042); translation from Usp. Mat. Nauk 59, No. 1, 187--188 (2004) Full Text: DOI
Pogrebkov, A. K. The boson-fermion correspondence and quantum integrable and dispersionless models. (English. Russian original) Zbl 1063.81065 Russ. Math. Surv. 58, No. 5, 1003-1037 (2003); translation from Usp. Mat. Nauk 58, No. 5, 163-196 (2003). MSC: 81R12 81T10 35Q53 37K10 81R10 PDFBibTeX XMLCite \textit{A. K. Pogrebkov}, Russ. Math. Surv. 58, No. 5, 1003--1037 (2003; Zbl 1063.81065); translation from Usp. Mat. Nauk 58, No. 5, 163--196 (2003) Full Text: DOI
Bukhshtaber, V. M.; Shorina, S. Yu. [Buchstaber, V. M.] The \(w\)-function of a solution of the \(g\)th stationary KdV equation. (English. Russian original) Zbl 1060.37054 Russ. Math. Surv. 58, No. 4, 780-781 (2003); translation from Usp. Mat. Nauk 58, No. 4, 145-146 (2003). Reviewer: Ma Wen-Xiu (Tampa) MSC: 37K10 35Q53 37K20 PDFBibTeX XMLCite \textit{V. M. Bukhshtaber} and \textit{S. Yu. Shorina}, Russ. Math. Surv. 58, No. 4, 780--781 (2003; Zbl 1060.37054); translation from Usp. Mat. Nauk 58, No. 4, 145--146 (2003) Full Text: DOI
Bukhshtaber, V. M.; Shorina, S. Yu. [Buchstaber, V. M.] Third-order commuting multidimensional differential operators that specify the KdV hierarchy. (English. Russian original) Zbl 1056.37509 Russ. Math. Surv. 58, No. 3, 610-612 (2003); translation from Usp. Mat. Nauk 58, No. 3, 187-188 (2003). MSC: 37K10 PDFBibTeX XMLCite \textit{V. M. Bukhshtaber} and \textit{S. Yu. Shorina}, Russ. Math. Surv. 58, No. 3, 610--612 (2003; Zbl 1056.37509); translation from Usp. Mat. Nauk 58, No. 3, 187--188 (2003) Full Text: DOI
Pavlov, M. V. New integrable \((2+1)\)-equations of hydrodynamic type. (English. Russian original) Zbl 1056.37082 Russ. Math. Surv. 58, No. 2, 384-385 (2003); translation from Usp. Mat. Nauk 58, No. 2, 171-172 (2003). Reviewer: Mircea Puta (Timişoara) MSC: 37K10 37N10 76A02 PDFBibTeX XMLCite \textit{M. V. Pavlov}, Russ. Math. Surv. 58, No. 2, 384--385 (2003; Zbl 1056.37082); translation from Usp. Mat. Nauk 58, No. 2, 171--172 (2003) Full Text: DOI
Igonin, S. A. Horizontal cohomology with coefficients, and nonlinear zero-curvature representations. (English. Russian original) Zbl 1056.37081 Russ. Math. Surv. 58, No. 1, 180-182 (2003); translation from Usp. Mat. Nauk 58, No. 1, 185-186 (2003). Reviewer: Mircea Puta (Timişoara) MSC: 37K10 58H10 PDFBibTeX XMLCite \textit{S. A. Igonin}, Russ. Math. Surv. 58, No. 1, 180--182 (2003; Zbl 1056.37081); translation from Usp. Mat. Nauk 58, No. 1, 185--186 (2003) Full Text: DOI
Mokhov, O. I. Lax pairs for compatible nonlocal Hamiltonian operators of hydrodynamic type. (English. Russian original) Zbl 1047.37051 Russ. Math. Surv. 57, No. 6, 1234-1235 (2002); translation from Usp. Mat. Nauk 57, No. 6, 189-190 (2002). Reviewer: Ding Tongren (Beijing) MSC: 37K15 37K10 PDFBibTeX XMLCite \textit{O. I. Mokhov}, Russ. Math. Surv. 57, No. 6, 1234--1235 (2002; Zbl 1047.37051); translation from Usp. Mat. Nauk 57, No. 6, 189--190 (2002) Full Text: DOI
Shorina, S. Yu. \(\wp\)-functions and Hamiltonian systems. (English. Russian original) Zbl 1042.37054 Russ. Math. Surv. 57, No. 5, 1007-1009 (2002); translation from Usp. Mat. Nauk 57, No. 5, 167-168 (2002). MSC: 37K20 37J35 70G55 14H40 35Q53 PDFBibTeX XMLCite \textit{S. Yu. Shorina}, Russ. Math. Surv. 57, No. 5, 1007--1009 (2002; Zbl 1042.37054); translation from Usp. Mat. Nauk 57, No. 5, 167--168 (2002) Full Text: DOI
Mokhov, O. I. Integrable bi-Hamiltonian hierarchies generated by compatible metrics of constant Riemannian curvature. (English. Russian original) Zbl 1042.37530 Russ. Math. Surv. 57, No. 5, 999-1001 (2002); translation from Usp. Mat. Nauk 57, No. 5, 157-158 (2002). MSC: 37K10 37K25 53B20 37N10 37K15 PDFBibTeX XMLCite \textit{O. I. Mokhov}, Russ. Math. Surv. 57, No. 5, 999--1001 (2002; Zbl 1042.37530); translation from Usp. Mat. Nauk 57, No. 5, 157--158 (2002) Full Text: DOI
Mokhov, O. I. Integrable bi-Hamiltonian systems of hydrodynamic type. (English. Russian original) Zbl 1044.37047 Russ. Math. Surv. 57, No. 1, 153-154 (2002); translation from Usp. Mat. Nauk 57, No. 1, 157-158 (2002). Reviewer: Ma Wen-Xiu (Tampa) MSC: 37K10 37K05 PDFBibTeX XMLCite \textit{O. I. Mokhov}, Russ. Math. Surv. 57, No. 1, 153--154 (2002; Zbl 1044.37047); translation from Usp. Mat. Nauk 57, No. 1, 157--158 (2002) Full Text: DOI
Suetin, S. P. On the dynamics of “wandering” zeros of polynomials orthogonal on some segments. (English. Russian original) Zbl 1117.30302 Russ. Math. Surv. 57, No. 2, 425-427 (2002); translation from Usp. Mat. Nauk 57, No. 2, 199-200 (2002). MSC: 30C10 30C15 37J35 37K20 PDFBibTeX XMLCite \textit{S. P. Suetin}, Russ. Math. Surv. 57, No. 2, 425--427 (2002; Zbl 1117.30302); translation from Usp. Mat. Nauk 57, No. 2, 199--200 (2002) Full Text: DOI
Chekhov, L. O. Integrable deformations of systems on graphs with loops. (English. Russian original) Zbl 1042.37053 Russ. Math. Surv. 57, No. 3, 587-588 (2002); translation from Usp. Mat. Nauk 57, No. 3, 169-170 (2002). MSC: 37K15 34B45 37K10 PDFBibTeX XMLCite \textit{L. O. Chekhov}, Russ. Math. Surv. 57, No. 3, 587--588 (2002; Zbl 1042.37053); translation from Usp. Mat. Nauk 57, No. 3, 169--170 (2002) Full Text: DOI arXiv
Mokhov, O. I. A Lax pair for nonsingular pencils of metrics of constant Riemannian curvature. (English. Russian original) Zbl 1042.37055 Russ. Math. Surv. 57, No. 3, 603-605 (2002); translation from Usp. Mat. Nauk 57, No. 3, 155-156 (2002). MSC: 37K25 53C20 PDFBibTeX XMLCite \textit{O. I. Mokhov}, Russ. Math. Surv. 57, No. 3, 603--605 (2002; Zbl 1042.37055); translation from Usp. Mat. Nauk 57, No. 3, 155--156 (2002) Full Text: DOI
Mokhov, O. I. Compatible Dubrovin-Novikov Hamiltonian operators and the Lie derivative. (English. Russian original) Zbl 1049.37518 Russ. Math. Surv. 56, No. 6, 1175-1176 (2001); translation from Usp. Mat. Nauk 56, No. 6, 161-162 (2001). MSC: 37K05 37K10 PDFBibTeX XMLCite \textit{O. I. Mokhov}, Russ. Math. Surv. 56, No. 6, 1175--1176 (2001; Zbl 1049.37518); translation from Usp. Mat. Nauk 56, No. 6, 161--162 (2001)
Treibich, A. Hyperelliptic tangential covers and finite-gap potentials. (English. Russian original) Zbl 1062.14044 Russ. Math. Surv. 56, No. 6, 1107-1151 (2001); translation from Usp. Mat. Nauk 56, No. 6, 89-136 (2001). Reviewer: Werner Kleinert (Berlin) MSC: 14H70 37K20 35Q53 37K10 14H30 14H42 PDFBibTeX XMLCite \textit{A. Treibich}, Russ. Math. Surv. 56, No. 6, 1107--1151 (2001; Zbl 1062.14044); translation from Usp. Mat. Nauk 56, No. 6, 89--136 (2001)
Balandin, A. V.; Potëmin, G. V. On nondegenerate differential-geometric Poisson brackets of third order. (English. Russian original) Zbl 1049.37516 Russ. Math. Surv. 56, No. 5, 976-977 (2001); translation from Usp. Mat. Nauk 56, No. 5, 177-178 (2001). MSC: 37J35 53D17 37K05 PDFBibTeX XMLCite \textit{A. V. Balandin} and \textit{G. V. Potëmin}, Russ. Math. Surv. 56, No. 5, 976--977 (2001; Zbl 1049.37516); translation from Usp. Mat. Nauk 56, No. 5, 177--178 (2001) Full Text: DOI
Natanzon, S. M. Formal series for the \(\tau\)-function realizing Riemann’s theorem about domains in the complex plane. (English. Russian original) Zbl 1114.37306 Russ. Math. Surv. 56, No. 4, 760-761 (2001); translation from Usp. Mat. Nauk 56, No. 4, 155-156 (2001). Reviewer: Messoud A. Efendiev (Berlin) MSC: 37K10 37K20 PDFBibTeX XMLCite \textit{S. M. Natanzon}, Russ. Math. Surv. 56, No. 4, 760--761 (2001; Zbl 1114.37306); translation from Usp. Mat. Nauk 56, No. 4, 155--156 (2001) Full Text: DOI
Zhiber, A. V.; Sokolov, V. V. Exactly integrable hyperbolic equations of Liouville type. (English. Russian original) Zbl 1003.35093 Russ. Math. Surv. 56, No. 1, 61-101 (2001); translation from Usp. Mat. Nauk 56, No. 1, 63-106 (2001). Reviewer: Xianguo Geng (Zhengzhou) MSC: 35L70 35A22 35A30 35Q53 37K35 58J70 37K10 PDFBibTeX XMLCite \textit{A. V. Zhiber} and \textit{V. V. Sokolov}, Russ. Math. Surv. 56, No. 1, 61--101 (2001; Zbl 1003.35093); translation from Usp. Mat. Nauk 56, No. 1, 63--106 (2001) Full Text: DOI
Chekhov, L. O.; Puzyrnikova, N. V. Integrable systems on graphs. (English. Russian original) Zbl 0999.37047 Russ. Math. Surv. 55, No. 5, 992-994 (2000); translation from Usp. Mat. Nauk 55, No. 5, 181-182 (2000). Reviewer: Mircea Puta (Timişoara) MSC: 37K10 37J35 34B45 PDFBibTeX XMLCite \textit{L. O. Chekhov} and \textit{N. V. Puzyrnikova}, Russ. Math. Surv. 55, No. 5, 992--994 (2000; Zbl 0999.37047); translation from Usp. Mat. Nauk 55, No. 5, 181--182 (2000) Full Text: DOI
Dovbysh, S. A. Intersection of separatrices and the non-integrability of multidimensional systems. (English. Russian original) Zbl 1057.37507 Russ. Math. Surv. 55, No. 3, 574-575 (2000); translation from Usp. Mat. Nauk 55, No. 3, 179-180 (2000). MSC: 37J30 37D05 34C37 37B10 37C99 37D10 PDFBibTeX XMLCite \textit{S. A. Dovbysh}, Russ. Math. Surv. 55, No. 3, 574--575 (2000; Zbl 1057.37507); translation from Usp. Mat. Nauk 55, No. 3, 179--180 (2000) Full Text: DOI
Krichever, I. M.; Novikov, S. P. Holomorphic bundles and scalar difference operators: single-point constructions. (English. Russian original) Zbl 1101.14315 Russ. Math. Surv. 55, No. 1, 180-181 (2000); translation from Usp. Mat. Nauk 55, No. 1, 187-188 (2000). MSC: 14H70 37K20 37K10 PDFBibTeX XMLCite \textit{I. M. Krichever} and \textit{S. P. Novikov}, Russ. Math. Surv. 55, No. 1, 187--188 (2000; Zbl 1101.14315); translation from Usp. Mat. Nauk 55, No. 1, 187--188 (2000) Full Text: DOI arXiv
Krichever, I. M.; Novikov, S. P. Trivalent graphs and solitons. (English. Russian original) Zbl 0981.37023 Russ. Math. Surv. 54, No. 6, 1248-1249 (1999); translation from Usp. Mat. Nauk 54, No. 6, 149-150 (1999). MSC: 37K10 35Q51 37K40 37K60 05C05 PDFBibTeX XMLCite \textit{I. M. Krichever} and \textit{S. P. Novikov}, Russ. Math. Surv. 54, No. 6, 149--150 (1999; Zbl 0981.37023); translation from Usp. Mat. Nauk 54, No. 6, 149--150 (1999) Full Text: DOI arXiv
Mal’tsev, A. Ya. Non-local Poisson brackets and Whitham’s method. (English. Russian original) Zbl 0967.37042 Russ. Math. Surv. 54, No. 6, 1252-1253 (1999); translation from Usp. Mat. Nauk 54, No. 6, 167-168 (1999). Reviewer: Mircea Puta (Timişoara) MSC: 37K10 37K40 PDFBibTeX XMLCite \textit{A. Ya. Mal'tsev}, Russ. Math. Surv. 54, No. 6, 167--168 (1999; Zbl 0967.37042); translation from Usp. Mat. Nauk 54, No. 6, 167--168 (1999) Full Text: DOI
Bolsinov, A. V.; Taĭmanov, I. A. On an example of an integrable geodesic flow with positive topological entropy. (English. Russian original) Zbl 1058.37520 Russ. Math. Surv. 54, No. 4, 833-834 (1999); translation from Usp. Mat. Nauk 54, No. 4, 157-158 (1999). Reviewer: Vladimir S. Matveev (MR1741286) MSC: 37J30 37B40 37J35 53D25 70H06 70H33 PDFBibTeX XMLCite \textit{A. V. Bolsinov} and \textit{I. A. Taĭmanov}, Russ. Math. Surv. 54, No. 4, 833--834 (1999; Zbl 1058.37520); translation from Usp. Mat. Nauk 54, No. 4, 157--158 (1999) Full Text: DOI
Repovš, D.; Skopenkov, A. B. Obstructions for Seifert fibrations and an extension of the Bolsinov-Fomenko theorem on integrable Hamiltonian systems. (English. Russian original) Zbl 0978.37048 Russ. Math. Surv. 54, No. 3, 652-653 (1999); translation from Usp. Mat. Nauk 54, No. 3, 181-182 (1999). Reviewer: Willy Sarlet (Gent) MSC: 37J35 55S35 37J30 57N10 70H05 PDFBibTeX XMLCite \textit{D. Repovš} and \textit{A. B. Skopenkov}, Russ. Math. Surv. 54, No. 3, 652--653 (1999; Zbl 0978.37048); translation from Usp. Mat. Nauk 54, No. 3, 181--182 (1999) Full Text: DOI
Lelekov, R. A. Necessary and sufficient conditions for convergence of conditional mathematical expectations relative to a \(\sigma\)-algebra. (English. Russian original) Zbl 0946.60023 Russ. Math. Surv. 53, No. 6, 1358-1359 (1998); translation from Usp. Mat. Nauk 53, No. 6, 255-256 (1998). Reviewer: R.J.Tomkins (Regina) MSC: 60F15 60F25 PDFBibTeX XMLCite \textit{R. A. Lelekov}, Russ. Math. Surv. 53, No. 6, 1358--1359 (1998; Zbl 0946.60023); translation from Usp. Mat. Nauk 53, No. 6, 255--256 (1998) Full Text: DOI
Dobrokhotov, S. Yu. Integrability by quadratures of Hamiltonian \(2n\)-dimensional systems with \(n\) known skew-orthogonal solutions. (English. Russian original) Zbl 0929.70014 Russ. Math. Surv. 53, No. 2, 380-381 (1998); translation from Usp. Mat. Nauk 53, No. 2, 143-144 (1998). Reviewer: Hubert Kalf (München) MSC: 70H06 37N05 37J35 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov}, Russ. Math. Surv. 53, No. 2, 380--381 (1998; Zbl 0929.70014); translation from Usp. Mat. Nauk 53, No. 2, 143--144 (1998) Full Text: DOI
Bolsinov, A. V. Fomenko invariants in the theory of integrable Hamiltonian systems. (English. Russian original) Zbl 0920.58027 Russ. Math. Surv. 52, No. 5, 997-1015 (1997); translation from Usp. Mat. Nauk 52, No. 5, 113-132 (1997). Reviewer: Messoud Efendiev (Berlin) MSC: 37J35 37K10 37J99 70H05 PDFBibTeX XMLCite \textit{A. V. Bolsinov}, Russ. Math. Surv. 52, No. 5, 997--1015 (1997; Zbl 0920.58027); translation from Usp. Mat. Nauk 52, No. 5, 113--132 (1997) Full Text: DOI
Arnol’d, V. I. Topological problems of the theory of wave propagation. (English. Russian original) Zbl 1053.37500 Russ. Math. Surv. 51, No. 1, 1-47 (1996); translation from Usp. Mat. Nauk 51, No. 1, 3-50 (1996). MSC: 37-02 37J35 58C35 PDFBibTeX XMLCite \textit{V. I. Arnol'd}, Russ. Math. Surv. 51, No. 1, 1--47 (1996; Zbl 1053.37500); translation from Usp. Mat. Nauk 51, No. 1, 3--50 (1996) Full Text: DOI
Ganzha, E. I.; Tsarev, S. P. An algebraic formula for superposition and the completeness of the Bäcklund transformations of (2+1)-dimensional integrable systems. (English. Russian original) Zbl 0887.35144 Russ. Math. Surv. 51, No. 6, 1200-1202 (1996); translation from Usp. Mat. Nauk 51, No. 6, 197-198 (1996). MSC: 35Q58 37J35 37K10 58J72 PDFBibTeX XMLCite \textit{E. I. Ganzha} and \textit{S. P. Tsarev}, Russ. Math. Surv. 51, No. 6, 1200--1202 (1996; Zbl 0887.35144); translation from Usp. Mat. Nauk 51, No. 6, 197--198 (1996) Full Text: DOI
Yakubov, V. Ya. Reconstruction of a Sturm-Liouville equation with an integrable weight. (English. Russian original) Zbl 0871.34017 Russ. Math. Surv. 51, No. 4, 758-759 (1996); translation from Usp. Mat. Nauk 51, No. 4, 175-176 (1996). MSC: 34B24 PDFBibTeX XMLCite \textit{V. Ya. Yakubov}, Russ. Math. Surv. 51, No. 4, 758--759 (1996; Zbl 0871.34017); translation from Usp. Mat. Nauk 51, No. 4, 175--176 (1996) Full Text: DOI
Dovbysh, S. A. Transversal intersection of separatrices, the structure of the set of quasi-stochastic motions and the non-existence of an analytic integral in multidimensional systems. (English. Russian original) Zbl 0877.58034 Russ. Math. Surv. 51, No. 4, 730-731 (1996); translation from Usp. Mat. Nauk 51, No. 4, 153-154 (1996). Reviewer: Y.Kifer (Jerusalem) MSC: 37J35 37K10 34C37 37E99 PDFBibTeX XMLCite \textit{S. A. Dovbysh}, Russ. Math. Surv. 51, No. 4, 730--731 (1996; Zbl 0877.58034); translation from Usp. Mat. Nauk 51, No. 4, 153--154 (1996) Full Text: DOI
Mordasheva, T. L. Canonical coordinates on orbits of a co-adjoint representation of certain semidirect products of Lie groups. (English. Russian original) Zbl 0893.58031 Russ. Math. Surv. 50, No. 6, 1282-1283 (1995); translation from Usp. Mat. Nauk 50, No. 6, 193-194 (1995). MSC: 37J35 37K10 PDFBibTeX XMLCite \textit{T. L. Mordasheva}, Russ. Math. Surv. 50, No. 6, 1282--1283 (1995; Zbl 0893.58031); translation from Usp. Mat. Nauk 50, No. 6, 193--194 (1995) Full Text: DOI
Golubeva, V. A.; Leksin, V. P. Complete integrability of generalized Knizhnik-Zamolodchikov equations of trigonometric type. (English. Russian original) Zbl 0873.17023 Russ. Math. Surv. 50, No. 3, 615-617 (1995); translation from Usp. Mat. Nauk 50, No. 3, 151-152 (1995). Reviewer: A.Rudy (Minsk) MSC: 17B67 35Q58 17B20 PDFBibTeX XMLCite \textit{V. A. Golubeva} and \textit{V. P. Leksin}, Russ. Math. Surv. 50, No. 3, 615--617 (1995; Zbl 0873.17023); translation from Usp. Mat. Nauk 50, No. 3, 151--152 (1995) Full Text: DOI
Bolsinov, A. V.; Kozlov, V. V.; Fomenko, A. T. The Maupertuis principle and geodesic flows on the sphere arising from integrable cases in the dynamics of a rigid body. (English. Russian original) Zbl 0881.58031 Russ. Math. Surv. 50, No. 3, 473-501 (1995); translation from Usp. Mat. Nauk 50, No. 3, 3-32 (1995). Reviewer: D.Hurley (Cork) MSC: 37J35 37K10 37D40 53D25 PDFBibTeX XMLCite \textit{A. V. Bolsinov} et al., Russ. Math. Surv. 50, No. 3, 473--501 (1995; Zbl 0881.58031); translation from Usp. Mat. Nauk 50, No. 3, 3--32 (1995) Full Text: DOI
Kalashnikov, V. V. Topological classification of quadratic-integrable geodesic flows on a two-dimensional torus. (English. Russian original) Zbl 0992.37501 Russ. Math. Surv. 50, No. 1, 200-201 (1995); translation from Usp. Mat. Nauk 50, No. 1, 201-202 (1995). Reviewer: J.S.Joel (Kelly) MSC: 37J35 37D40 PDFBibTeX XMLCite \textit{V. V. Kalashnikov}, Russ. Math. Surv. 50, No. 1, 200--201 (1995; Zbl 0992.37501); translation from Usp. Mat. Nauk 50, No. 1, 201--202 (1995) Full Text: DOI
Bukhshtaber, V. M.; Ènol’skiĭ, V. Z. Abelian Bloch solutions of the two-dimensional Schrödinger equation. (English. Russian original) Zbl 0847.35091 Russ. Math. Surv. 50, No. 1, 195-197 (1995); translation from Usp. Mat. Nauk 50, No. 1, 191-192 (1995). Reviewer: Oleg Titow (Berlin) MSC: 35Q99 35Q55 14K25 37J35 PDFBibTeX XMLCite \textit{V. M. Bukhshtaber} and \textit{V. Z. Ènol'skiĭ}, Russ. Math. Surv. 50, No. 1, 195--197 (1995; Zbl 0847.35091); translation from Usp. Mat. Nauk 50, No. 1, 191--192 (1995) Full Text: DOI
Bolsinov, A. V.; Fomenko, A. T. A criterion for the topological conjugacy of Hamiltonian flows on two-dimensional compact surfaces. (English. Russian original) Zbl 0992.37500 Russ. Math. Surv. 50, No. 1, 193-194 (1995); translation from Usp. Mat. Nauk 50, No. 1, 189-190 (1995). Reviewer: J.S.Joel (Kelly) MSC: 37J35 70H05 PDFBibTeX XMLCite \textit{A. V. Bolsinov} and \textit{A. T. Fomenko}, Russ. Math. Surv. 50, No. 1, 193--194 (1995; Zbl 0992.37500); translation from Usp. Mat. Nauk 50, No. 1, 189--190 (1995) Full Text: DOI
Trofimov, V. V. Canonical coordinates on orbits of the coadjoint representation of tensorial extensions of Lie groups. (English. Russian original) Zbl 0858.58018 Russ. Math. Surv. 49, No. 1, 251-253 (1994); translation from Usp. Mat. Nauk 49, No. 1(295), 229-230 (1994). Reviewer: E.Previato (Boston) MSC: 37J99 37J35 37K10 17B99 22E45 53C05 PDFBibTeX XMLCite \textit{V. V. Trofimov}, Russ. Math. Surv. 49, No. 1, 1 (1994; Zbl 0858.58018); translation from Usp. Mat. Nauk 49, No. 1(295), 229--230 (1994) Full Text: DOI
Trofimov, V. V. The relative symplectic volume on orbits of a coadjoint representation of simple Lie groups. (English. Russian original) Zbl 0842.58036 Russ. Math. Surv. 48, No. 6, 185-186 (1993); translation from Usp. Mat. Nauk 48, No. 6(294), 173-174 (1993). Reviewer: J.Koiller (Rio de Janeiro) MSC: 37J99 37J35 37K10 PDFBibTeX XMLCite \textit{V. V. Trofimov}, Russ. Math. Surv. 48, No. 6, 1 (1993; Zbl 0842.58036); translation from Usp. Mat. Nauk 48, No. 6(294), 173--174 (1993) Full Text: DOI
Orel, O. E. Topological analysis of a neighbourhood of a degenerate one-dimensional orbit of the Poisson action of \(\mathbb{R}^ 2\) on the symplectic manifold \(M^ 4\). (English. Russian original) Zbl 0834.58024 Russ. Math. Surv. 48, No. 6, 176-177 (1993); translation from Usp. Mat. Nauk 48, No. 6(294), 165-166 (1993). Reviewer: Yu.E.Gliklikh (Voronezh) MSC: 37J35 37K10 37J99 54H20 PDFBibTeX XMLCite \textit{O. E. Orel}, Russ. Math. Surv. 48, No. 6, 1 (1993; Zbl 0834.58024); translation from Usp. Mat. Nauk 48, No. 6(294), 165--166 (1993) Full Text: DOI
Bolsinov, A. V.; Fomenko, A. T. Trajectory classification of integrable systems of Euler type in the dynamics of a rigid body. (English. Russian original) Zbl 0820.58029 Russ. Math. Surv. 48, No. 5, 165-166 (1993); translation from Usp. Mat. Nauk 48, No. 5(293), 163-164 (1993). Reviewer: W.M.Oliva (Lisboa) MSC: 37J35 37K10 37J99 PDFBibTeX XMLCite \textit{A. V. Bolsinov} and \textit{A. T. Fomenko}, Russ. Math. Surv. 48, No. 5, 163--164 (1993; Zbl 0820.58029); translation from Usp. Mat. Nauk 48, No. 5(293), 163--164 (1993) Full Text: DOI
Selivanova, E. N. A topological portrait of certain multidimensional Hamiltonian systems. (English. Russian original) Zbl 0802.58032 Russ. Math. Surv. 48, No. 2, 204-205 (1993); translation from Usp. Mat. Nauk 48, No. 2(290), 199-200 (1993). Reviewer: M.Baake (Tübingen) MSC: 37J35 37K10 PDFBibTeX XMLCite \textit{E. N. Selivanova}, Russ. Math. Surv. 48, No. 2, 1 (1993; Zbl 0802.58032); translation from Usp. Mat. Nauk 48, No. 2(290), 199--200 (1993) Full Text: DOI
Isaenko, E. M. An explicit description of a model of a \(\mathcal G\)-invariant magnet. (English. Russian original) Zbl 0821.58022 Russ. Math. Surv. 48, No. 2, 186-187 (1993); translation from Usp. Mat. Nauk 48, No. 2(290), 187-188 (1993). Reviewer: H.D.Voulov (Sofia) MSC: 37J35 37K10 35Q55 PDFBibTeX XMLCite \textit{E. M. Isaenko}, Russ. Math. Surv. 48, No. 2, 1 (1993; Zbl 0821.58022); translation from Usp. Mat. Nauk 48, No. 2(290), 187--188 (1993) Full Text: DOI