Bolsinov, Alexey V.; Konyaev, Andrey Yu; Matveev, Vladimir S. Applications of Nijenhuis geometry. II: Maximal pencils of multi-Hamiltonian structures of hydrodynamic type. (English) Zbl 1475.37075 Nonlinearity 34, No. 8, 5136-5162 (2021). Reviewer: Ivan C. Sterling (St. Mary’s City) MSC: 37K25 37K06 37K10 53D17 PDF BibTeX XML Cite \textit{A. V. Bolsinov} et al., Nonlinearity 34, No. 8, 5136--5162 (2021; Zbl 1475.37075) Full Text: DOI arXiv OpenURL
Ontani, Riccardo Some remarks on the operator formalism for nonlocal Poisson brackets. (English) Zbl 1454.53065 J. Math. Phys. 61, No. 9, 093506, 16 p. (2020). MSC: 53D17 PDF BibTeX XML Cite \textit{R. Ontani}, J. Math. Phys. 61, No. 9, 093506, 16 p. (2020; Zbl 1454.53065) Full Text: DOI arXiv OpenURL
Meleshko, S. V. Complete group classification of the two-dimensional shallow water equations with constant Coriolis parameter in Lagrangian coordinates. (English) Zbl 1450.35022 Commun. Nonlinear Sci. Numer. Simul. 89, Article ID 105293, 9 p. (2020). MSC: 35B06 35Q35 35Q86 PDF BibTeX XML Cite \textit{S. V. Meleshko}, Commun. Nonlinear Sci. Numer. Simul. 89, Article ID 105293, 9 p. (2020; Zbl 1450.35022) Full Text: DOI OpenURL
Mokhov, O. I. On metrics of diagonal curvature. (English. Russian original) Zbl 1448.53017 J. Math. Sci., New York 248, No. 6, 780-787 (2020); translation from Fundam. Prikl. Mat. 21, No. 6, 171-182 (2016). MSC: 53B20 PDF BibTeX XML Cite \textit{O. I. Mokhov}, J. Math. Sci., New York 248, No. 6, 780--787 (2020; Zbl 1448.53017); translation from Fundam. Prikl. Mat. 21, No. 6, 171--182 (2016) Full Text: DOI OpenURL
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 PDF BibTeX XML Cite \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 OpenURL
Odesskii, Alexander Poisson structures on loop spaces of \(\mathbb{C} P^n\) and an \(r\)-matrix associated with the universal elliptic curve. (English) Zbl 1446.53066 J. Geom. Phys. 140, 152-160 (2019). Reviewer: Andrew Bruce (Esch-sur-Alzette) MSC: 53D17 14H52 PDF BibTeX XML Cite \textit{A. Odesskii}, J. Geom. Phys. 140, 152--160 (2019; Zbl 1446.53066) Full Text: DOI arXiv OpenURL
Casati, M.; Ferapontov, E. V.; Pavlov, M. V.; Vitolo, R. F. On a class of third-order nonlocal Hamiltonian operators. (English) Zbl 1420.37049 J. Geom. Phys. 138, 285-296 (2019). MSC: 37K05 37K10 37K20 37K25 PDF BibTeX XML Cite \textit{M. Casati} et al., J. Geom. Phys. 138, 285--296 (2019; Zbl 1420.37049) Full Text: DOI arXiv OpenURL
Mokhov, O. I.; Pavlenko, N. A. Classification of the associativity equations with a first-order Hamiltonian operator. (English. Russian original) Zbl 1407.81098 Theor. Math. Phys. 197, No. 1, 1501-1513 (2018); translation from Teor. Mat. Fiz. 197, No. 1, 121-137 (2018). MSC: 81Q10 81T40 81T45 35Q35 PDF BibTeX XML Cite \textit{O. I. Mokhov} and \textit{N. A. Pavlenko}, Theor. Math. Phys. 197, No. 1, 1501--1513 (2018; Zbl 1407.81098); translation from Teor. Mat. Fiz. 197, No. 1, 121--137 (2018) Full Text: DOI OpenURL
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 PDF BibTeX XML Cite \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 OpenURL
Ferapontov, Evgeny V.; Pavlov, Maxim V.; Vitolo, Raffaele F. Systems of conservation laws with third-order Hamiltonian structures. (English) Zbl 1392.37050 Lett. Math. Phys. 108, No. 6, 1525-1550 (2018). Reviewer: Tihomir Valchev (Sofia) MSC: 37K05 37K10 37K20 37K25 PDF BibTeX XML Cite \textit{E. V. Ferapontov} et al., Lett. Math. Phys. 108, No. 6, 1525--1550 (2018; Zbl 1392.37050) Full Text: DOI arXiv OpenURL
Lorenzoni, P.; Savoldi, A.; Vitolo, R. Bi-Hamiltonian structures of KdV type. (English) Zbl 1396.37073 J. Phys. A, Math. Theor. 51, No. 4, Article ID 045202, 16 p. (2018). Reviewer: Ma Wen-Xiu (Tampa) MSC: 37K10 37K05 35Q53 37K25 PDF BibTeX XML Cite \textit{P. Lorenzoni} et al., J. Phys. A, Math. Theor. 51, No. 4, Article ID 045202, 16 p. (2018; Zbl 1396.37073) Full Text: DOI arXiv OpenURL
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 PDF BibTeX XML Cite \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 OpenURL
Pavlov, M. V.; Vitolo, R. F. Remarks on the Lagrangian representation of bi-Hamiltonian equations. (English) Zbl 1358.37107 J. Geom. Phys. 113, 239-249 (2017). MSC: 37K05 37K10 37K20 37K25 PDF BibTeX XML Cite \textit{M. V. Pavlov} and \textit{R. F. Vitolo}, J. Geom. Phys. 113, 239--249 (2017; Zbl 1358.37107) Full Text: DOI arXiv OpenURL
Sheftel, Mikhail B.; Yazıcı, Devrim Recursion operators and tri-Hamiltonian structure of the first heavenly equation of Plebański. (English) Zbl 1346.35194 SIGMA, Symmetry Integrability Geom. Methods Appl. 12, Paper 091, 17 p. (2016). MSC: 35Q75 83C15 37K05 37K10 PDF BibTeX XML Cite \textit{M. B. Sheftel} and \textit{D. Yazıcı}, SIGMA, Symmetry Integrability Geom. Methods Appl. 12, Paper 091, 17 p. (2016; Zbl 1346.35194) Full Text: DOI arXiv OpenURL
Savoldi, Andrea On deformations of one-dimensional Poisson structures of hydrodynamic type with degenerate metric. (English) Zbl 1334.37076 J. Geom. Phys. 104, 246-276 (2016). MSC: 37K05 37K25 PDF BibTeX XML Cite \textit{A. Savoldi}, J. Geom. Phys. 104, 246--276 (2016; Zbl 1334.37076) Full Text: DOI arXiv OpenURL
Pavlov, Maxim V.; Vitolo, Raffaele F. On the bi-Hamiltonian geometry of WDVV equations. (English) Zbl 1332.37048 Lett. Math. Phys. 105, No. 8, 1135-1163 (2015). Reviewer: Vladislav Nikolaevich Dumachev (Voronezh) MSC: 37K05 37K10 37K20 37K25 PDF BibTeX XML Cite \textit{M. V. Pavlov} and \textit{R. F. Vitolo}, Lett. Math. Phys. 105, No. 8, 1135--1163 (2015; Zbl 1332.37048) Full Text: DOI arXiv OpenURL
Ferapontov, Evgeny V.; Lorenzoni, Paolo; Savoldi, Andrea Hamiltonian operators of Dubrovin-Novikov type in 2D. (English) Zbl 1310.37027 Lett. Math. Phys. 105, No. 3, 341-377 (2015). MSC: 37K05 37K10 37K25 53D45 PDF BibTeX XML Cite \textit{E. V. Ferapontov} et al., Lett. Math. Phys. 105, No. 3, 341--377 (2015; Zbl 1310.37027) Full Text: DOI arXiv Link OpenURL
Cirilo-Lombardo, D. J.; Gershun, V. D. Integrable hydrodynamic equations for initial chiral currents and infinite hydrodynamic chains from WZNW model and string model of WZNW type with \(SU(2), SO(3), SP(2), SU(\infty), SO(\infty), SP(\infty)\) constant torsions. (English) Zbl 1301.81251 Int. J. Mod. Phys. A 29, No. 24, Article ID 1450134, 30 p. (2014). MSC: 81T40 70G65 81T30 81R05 81T13 17B80 PDF BibTeX XML Cite \textit{D. J. Cirilo-Lombardo} and \textit{V. D. Gershun}, Int. J. Mod. Phys. A 29, No. 24, Article ID 1450134, 30 p. (2014; Zbl 1301.81251) Full Text: DOI arXiv OpenURL
Ferapontov, E. V.; Pavlov, M. V.; Vitolo, R. F. Projective-geometric aspects of homogeneous third-order Hamiltonian operators. (English) Zbl 1321.37071 J. Geom. Phys. 85, 16-28 (2014). Reviewer: Antonio De Nicola (Coimbra) MSC: 37K25 37K05 37K10 53A20 PDF BibTeX XML Cite \textit{E. V. Ferapontov} et al., J. Geom. Phys. 85, 16--28 (2014; Zbl 1321.37071) Full Text: DOI arXiv OpenURL
Parodi, E. On classification of discrete, scalar-valued Poisson brackets. (English) Zbl 1247.53095 J. Geom. Phys. 62, No. 10, 2059-2076 (2012). Reviewer: Angela Gammella-Mathieu (Metz) MSC: 53D17 53C17 PDF BibTeX XML Cite \textit{E. Parodi}, J. Geom. Phys. 62, No. 10, 2059--2076 (2012; Zbl 1247.53095) Full Text: DOI arXiv OpenURL
Mokhov, O. I. Compatible metrics and the diagonalizability of nonlocally bi-Hamiltonian systems of hydrodynamic type. (English. Russian original) Zbl 1417.37232 Theor. Math. Phys. 167, No. 1, 403-420 (2011); translation from Teor. Mat. Fiz. 167, No. 1, 3-22 (2011). MSC: 37K10 37K25 PDF BibTeX XML Cite \textit{O. I. Mokhov}, Theor. Math. Phys. 167, No. 1, 403--420 (2011; Zbl 1417.37232); translation from Teor. Mat. Fiz. 167, No. 1, 3--22 (2011) Full Text: DOI arXiv OpenURL
Reynolds, A. P.; Bogoyavlenskij, O. I. Lie algebra structures for four-component Hamiltonian hydrodynamic type systems. (English) Zbl 1228.35139 J. Geom. Phys. 61, No. 12, 2400-2409 (2011). MSC: 35L60 37K05 PDF BibTeX XML Cite \textit{A. P. Reynolds} and \textit{O. I. Bogoyavlenskij}, J. Geom. Phys. 61, No. 12, 2400--2409 (2011; Zbl 1228.35139) Full Text: DOI OpenURL
Mokhov, O. I. Realization of Frobenius manifolds as submanifolds in pseudo-Euclidean spaces. (English. Russian original) Zbl 1242.53114 Proc. Steklov Inst. Math. 267, 217-234 (2009); translation from Trudy Mat. Inst. Steklova 267, 226-244 (2009). MSC: 53D45 53B25 53B30 PDF BibTeX XML Cite \textit{O. I. Mokhov}, Proc. Steklov Inst. Math. 267, 217--234 (2009; Zbl 1242.53114); translation from Trudy Mat. Inst. Steklova 267, 226--244 (2009) Full Text: DOI arXiv OpenURL
Mokhov, O. I. The classification of nonsingular multidimensional Dubrovin-Novikov brackets. (English) Zbl 1180.37088 Funct. Anal. Appl. 42, No. 1, 33-44 (2008); translation from Funkts. Anal. Prilozh. 42, No. 1, 39-52 (2008). Reviewer: Vladimir Răsvan (Craiova) MSC: 37K05 35F21 35L65 PDF BibTeX XML Cite \textit{O. I. Mokhov}, Funct. Anal. Appl. 42, No. 1, 33--44 (2008; Zbl 1180.37088); translation from Funkts. Anal. Prilozh. 42, No. 1, 39--52 (2008) Full Text: DOI arXiv Link OpenURL
Bogoyavlenskij, O.; Reynolds, P. Form-invariant Poisson brackets of hydrodynamic type with several spatial variables. (English) Zbl 1152.81346 J. Math. Phys. 49, No. 5, 053520, 15 p. (2008). MSC: 37K05 37K10 35F20 PDF BibTeX XML Cite \textit{O. Bogoyavlenskij} and \textit{P. Reynolds}, J. Math. Phys. 49, No. 5, 053520, 15 p. (2008; Zbl 1152.81346) Full Text: DOI OpenURL
Ferguson, James T. Flat pencils of symplectic connections and Hamiltonian operators of degree 2. (English) Zbl 1143.53071 J. Geom. Phys. 58, No. 4, 468-486 (2008). MSC: 53D05 37K10 37K05 PDF BibTeX XML Cite \textit{J. T. Ferguson}, J. Geom. Phys. 58, No. 4, 468--486 (2008; Zbl 1143.53071) Full Text: DOI arXiv OpenURL