Skrypnyk, T. Symmetric and asymmetric separated variables. II: A second integrable case of the complex Kirchhoff model. (English) Zbl 1521.37059 J. Math. Phys. 64, No. 9, Article ID 093503, 21 p. (2023). MSC: 37J35 37J38 70E40 PDFBibTeX XMLCite \textit{T. Skrypnyk}, J. Math. Phys. 64, No. 9, Article ID 093503, 21 p. (2023; Zbl 1521.37059) Full Text: DOI
Yakimova, Oksana A bi-Hamiltonian nature of the Gaudin algebras. (English) Zbl 1526.17041 Adv. Math. 412, Article ID 108805, 42 p. (2023). MSC: 17B63 17B65 17B80 PDFBibTeX XMLCite \textit{O. Yakimova}, Adv. Math. 412, Article ID 108805, 42 p. (2023; Zbl 1526.17041) Full Text: DOI arXiv
Gubarev, Vsevolod Universal enveloping algebra of a pair of compatible Lie brackets. (English) Zbl 1527.16027 Int. J. Algebra Comput. 32, No. 7, 1335-1344 (2022). Reviewer: Dmitry Artamonov (Moskva) MSC: 16S30 16Z10 17B35 PDFBibTeX XMLCite \textit{V. Gubarev}, Int. J. Algebra Comput. 32, No. 7, 1335--1344 (2022; Zbl 1527.16027) Full Text: DOI arXiv
Tempesta, Piergiulio; Tondo, Giorgio Haantjes algebras of classical integrable systems. (English) Zbl 1525.37060 Ann. Mat. Pura Appl. (4) 201, No. 1, 57-90 (2022); correction ibid. 201, No. 1, 91 (2022). MSC: 37J35 37J39 37J37 53D05 35Q53 PDFBibTeX XMLCite \textit{P. Tempesta} and \textit{G. Tondo}, Ann. Mat. Pura Appl. (4) 201, No. 1, 57--90 (2022; Zbl 1525.37060) Full Text: DOI arXiv
Skrypnyk, T. Symmetric and asymmetric separation of variables for an integrable case of the complex Kirchhoff’s problem. (English) Zbl 1484.35017 J. Geom. Phys. 172, Article ID 104418, 26 p. (2022). MSC: 35A30 37J35 PDFBibTeX XMLCite \textit{T. Skrypnyk}, J. Geom. Phys. 172, Article ID 104418, 26 p. (2022; Zbl 1484.35017) Full Text: DOI
Panyushev, Dmitri I.; Yakimova, Oksana S. Periodic automorphisms, compatible Poisson brackets, and Gaudin subalgebras. (English) Zbl 1511.17055 Transform. Groups 26, No. 2, 641-670 (2021). MSC: 17B63 17B08 17B20 22E46 PDFBibTeX XMLCite \textit{D. I. Panyushev} and \textit{O. S. Yakimova}, Transform. Groups 26, No. 2, 641--670 (2021; Zbl 1511.17055) Full Text: DOI arXiv
Guha, Partha; Mukherjee, Indranil Hierarchies and Hamiltonian structures of the nonlinear Schrödinger family using geometric and spectral techniques. (English) Zbl 1416.35238 Discrete Contin. Dyn. Syst., Ser. B 24, No. 4, 1677-1695 (2019). MSC: 35Q55 37K10 37K30 35P99 PDFBibTeX XMLCite \textit{P. Guha} and \textit{I. Mukherjee}, Discrete Contin. Dyn. Syst., Ser. B 24, No. 4, 1677--1695 (2019; Zbl 1416.35238) Full Text: DOI
Tondo, G. Haantjes algebras of the Lagrange top. (English. Russian original) Zbl 1431.70009 Theor. Math. Phys. 196, No. 3, 1366-1379 (2018); translation from Teor. Mat. Fiz. 196, No. 3, 487-502 (2018). MSC: 70H20 37J06 PDFBibTeX XMLCite \textit{G. Tondo}, Theor. Math. Phys. 196, No. 3, 1366--1379 (2018; Zbl 1431.70009); translation from Teor. Mat. Fiz. 196, No. 3, 487--502 (2018) Full Text: DOI arXiv
Kryński, Wojciech On deformations of the dispersionless Hirota equation. (English) Zbl 1392.35263 J. Geom. Phys. 127, 46-54 (2018). Reviewer: Ahmed Lesfari (El Jadida) MSC: 35Q53 37K10 58J72 37K35 53A60 53C28 53C25 PDFBibTeX XMLCite \textit{W. Kryński}, J. Geom. Phys. 127, 46--54 (2018; Zbl 1392.35263) Full Text: DOI arXiv
Bolsinov, A. V.; Izosimov, A. M.; Tsonev, D. M. Finite-dimensional integrable systems: a collection of research problems. (English) Zbl 1381.37068 J. Geom. Phys. 115, 2-15 (2017). Reviewer: Boris S. Kruglikov (Tromsø) MSC: 37J35 37J05 37J15 53D17 PDFBibTeX XMLCite \textit{A. V. Bolsinov} et al., J. Geom. Phys. 115, 2--15 (2017; Zbl 1381.37068) Full Text: DOI Link
Bolsinov, Alexey Some remarks about Mishchenko-Fomenko subalgebras. (English) Zbl 1418.17029 J. Algebra 483, 58-70 (2017). MSC: 17B35 PDFBibTeX XMLCite \textit{A. Bolsinov}, J. Algebra 483, 58--70 (2017; Zbl 1418.17029) Full Text: DOI arXiv
Izosimov, Anton Flat bi-Hamiltonian structures and invariant densities. (English) Zbl 1362.37112 Lett. Math. Phys. 106, No. 10, 1415-1427 (2016). Reviewer: Yuri E. Gliklikh (Voronezh) MSC: 37J35 37K10 53D17 37J15 37J05 PDFBibTeX XMLCite \textit{A. Izosimov}, Lett. Math. Phys. 106, No. 10, 1415--1427 (2016; Zbl 1362.37112) Full Text: DOI arXiv
Bolsinov, A. V.; Zhang, P. Jordan-Kronecker invariants of finite-dimensional Lie algebras. (English) Zbl 1387.17011 Transform. Groups 21, No. 1, 51-86 (2016). MSC: 17B08 17B63 PDFBibTeX XMLCite \textit{A. V. Bolsinov} and \textit{P. Zhang}, Transform. Groups 21, No. 1, 51--86 (2016; Zbl 1387.17011) Full Text: DOI arXiv
Zhang, Pumei Algebraic properties of compatible Poisson brackets. (English) Zbl 1316.15014 Regul. Chaotic Dyn. 19, No. 3, 267-288 (2014). Reviewer: Frank Uhlig (Auburn) MSC: 15A22 15A21 15A24 15A30 15A18 15A63 15B57 17B45 53D17 PDFBibTeX XMLCite \textit{P. Zhang}, Regul. Chaotic Dyn. 19, No. 3, 267--288 (2014; Zbl 1316.15014) Full Text: DOI
Bolsinov, Alexey; Izosimov, Anton Singularities of bi-Hamiltonian systems. (English) Zbl 1315.37040 Commun. Math. Phys. 331, No. 2, 507-543 (2014). Reviewer: Mohamed Selmi (Sousse-Riadh) MSC: 37K10 37K30 PDFBibTeX XMLCite \textit{A. Bolsinov} and \textit{A. Izosimov}, Commun. Math. Phys. 331, No. 2, 507--543 (2014; Zbl 1315.37040) Full Text: DOI arXiv Link
Batalin, Igor A.; Bering, Klaus A triplectic bi-Darboux theorem and para-hypercomplex geometry. (English) Zbl 1282.53069 J. Math. Phys. 53, No. 12, 123507, 25 p. (2012). Reviewer: Angela Gammella-Mathieu (Metz) MSC: 53D17 53C26 53D05 58A50 PDFBibTeX XMLCite \textit{I. A. Batalin} and \textit{K. Bering}, J. Math. Phys. 53, No. 12, 123507, 25 p. (2012; Zbl 1282.53069) Full Text: DOI arXiv
Odesskii, A. V.; Rubtsov, V. N.; Sokolov, V. V. Bi-Hamiltonian ordinary differential equations with matrix variables. (English. Russian original) Zbl 1274.70023 Theor. Math. Phys. 171, No. 1, 442-447 (2012); translation from Teor. Mat. Fiz. 171, No. 1, 26-32 (2012). MSC: 70H05 70H06 37J35 17B63 PDFBibTeX XMLCite \textit{A. V. Odesskii} et al., Theor. Math. Phys. 171, No. 1, 442--447 (2012; Zbl 1274.70023); translation from Teor. Mat. Fiz. 171, No. 1, 26--32 (2012) Full Text: DOI arXiv HAL
Falqui, Gregorio; Pedroni, Marco Poisson pencils, algebraic integrability, and separation of variables. (English) Zbl 1254.14040 Regul. Chaotic Dyn. 16, No. 3-4, 223-244 (2011). Reviewer: Ahmed Lesfari (El Jadida) MSC: 14H70 37J35 37K10 70H20 PDFBibTeX XMLCite \textit{G. Falqui} and \textit{M. Pedroni}, Regul. Chaotic Dyn. 16, No. 3--4, 223--244 (2011; Zbl 1254.14040) Full Text: DOI arXiv
Błaszak, Maciej Bi-presymplectic representation of Liouville integrable systems and related separability theory. (English) Zbl 1222.37054 Stud. Appl. Math. 126, No. 4, 319-346 (2011). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 37K10 PDFBibTeX XMLCite \textit{M. Błaszak}, Stud. Appl. Math. 126, No. 4, 319--346 (2011; Zbl 1222.37054) Full Text: DOI arXiv
Roubtsov, V.; Skrypnyk, T. Compatible Poisson brackets, quadratic Poisson algebras and classical \(r\)-matrices. (English) Zbl 1180.37106 Kruglikov, Boris (ed.) et al., Differential equations – Geometry, symmetries and integrability. The Abel symposium 2008. Proceedings of the fifth Abel symposium, Tromsø, Norway, June 17–22, 2008. Berlin: Springer (ISBN 978-3-642-00872-6/hbk; 978-3-642-00873-3/ebook). Abel Symposia 5, 311-333 (2009). MSC: 37K30 17B80 PDFBibTeX XMLCite \textit{V. Roubtsov} and \textit{T. Skrypnyk}, Abel Symp. 5, 311--333 (2009; Zbl 1180.37106) Full Text: DOI
Akivis, M. A.; Goldberg, V. V. Differential geometry of Veronese-like webs. (English) Zbl 1298.53014 Russ. Math. 51, No. 10, 1-28 (2007) and Izv. Vyssh. Uchebn. Zaved., Mat. 2007, No. 10, 3-28 (2007). MSC: 53A60 PDFBibTeX XMLCite \textit{M. A. Akivis} and \textit{V. V. Goldberg}, Russ. Math. 51, No. 10, 1--28 (2007; Zbl 1298.53014) Full Text: DOI
Falqui, Gregorio; Musso, Fabio On separation of variables for homogeneous \(sl(r)\) Gaudin systems. (English) Zbl 1255.70014 Math. Phys. Anal. Geom. 9, No. 3, 233-262 (2006). MSC: 70H06 70H20 37K10 PDFBibTeX XMLCite \textit{G. Falqui} and \textit{F. Musso}, Math. Phys. Anal. Geom. 9, No. 3, 233--262 (2006; Zbl 1255.70014) Full Text: DOI arXiv
Odesskii, A. V.; Sokolov, V. V. Compatible Lie brackets related to elliptic curve. (English) Zbl 1111.17008 J. Math. Phys. 47, No. 1, 013506, 14 p. (2006). MSC: 17B37 37J35 37K10 PDFBibTeX XMLCite \textit{A. V. Odesskii} and \textit{V. V. Sokolov}, J. Math. Phys. 47, No. 1, 013506, 14 p. (2006; Zbl 1111.17008) Full Text: DOI arXiv
Panasyuk, Andriy Algebraic Nijenhuis operators and Kronecker Poisson pencils. (English) Zbl 1114.53067 Differ. Geom. Appl. 24, No. 5, 482-491 (2006). MSC: 53D17 17B63 37J35 PDFBibTeX XMLCite \textit{A. Panasyuk}, Differ. Geom. Appl. 24, No. 5, 482--491 (2006; Zbl 1114.53067) Full Text: DOI arXiv
Akivis, M. A.; Gol’dberg, V. V.; Chakmazyan, A. V. Induced connections on manifolds in spaces with fundamental groups. (English. Russian original) Zbl 1109.53011 Russ. Math. 48, No. 10, 1-15 (2004); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2004, No. 10, 3-18 (2004). Reviewer: Erhard Heil (Darmstadt) MSC: 53A20 53A15 53B05 53A25 PDFBibTeX XMLCite \textit{M. A. Akivis} et al., Russ. Math. 48, No. 10, 1--15 (2004; Zbl 1109.53011); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2004, No. 10, 3--18 (2004) Full Text: DOI arXiv
Guha, Partha AKS hierarchy and bi-Hamiltonian geometry of Gelfand-Zakharevich type. (English) Zbl 1071.37044 J. Math. Phys. 45, No. 7, 2864-2884 (2004). MSC: 37K10 37K05 PDFBibTeX XMLCite \textit{P. Guha}, J. Math. Phys. 45, No. 7, 2864--2884 (2004; Zbl 1071.37044) Full Text: DOI
Damianou, Pantelis A. Multiple Hamiltonian structure of Bogoyavlensky-Toda lattices. (English) Zbl 1053.37061 Rev. Math. Phys. 16, No. 2, 175-241 (2004). Reviewer: Jan Chrastina (Brno) MSC: 37K60 37J35 37K10 70H06 PDFBibTeX XMLCite \textit{P. A. Damianou}, Rev. Math. Phys. 16, No. 2, 175--241 (2004; Zbl 1053.37061) Full Text: DOI arXiv
Sciacca, Vincenzo Discrete KP equation and momentum mapping of Toda system. (English) Zbl 1362.39014 J. Nonlinear Math. Phys. 10, Suppl. 2, 209-222 (2003). MSC: 39A12 37K10 35Q53 PDFBibTeX XMLCite \textit{V. Sciacca}, J. Nonlinear Math. Phys. 10, 209--222 (2003; Zbl 1362.39014) Full Text: DOI
Panasyuk, Andriy Projections of Jordan bi-Poisson structures that are Kronecker, diagonal actions, and the classical Gaudin systems. (English) Zbl 1038.53077 J. Geom. Phys. 47, No. 4, 379-397 (2003). Reviewer: Olga Radko (Los Angeles) MSC: 53D17 53D20 37J35 PDFBibTeX XMLCite \textit{A. Panasyuk}, J. Geom. Phys. 47, No. 4, 379--397 (2003; Zbl 1038.53077) Full Text: DOI arXiv
Damianou, Pantelis A. The negative Toda hierarchy and rational Poisson brackets. (English) Zbl 1010.37036 J. Geom. Phys. 45, No. 1-2, 184-202 (2003). MSC: 37J35 70H06 PDFBibTeX XMLCite \textit{P. A. Damianou}, J. Geom. Phys. 45, No. 1--2, 184--202 (2003; Zbl 1010.37036) Full Text: DOI
Foth, Philip Bruhat Poisson structure on \({\mathbb CP}^n\) and integrable systems. (English) Zbl 1059.53065 J. Math. Phys. 43, No. 6, 3124-3132 (2002). MSC: 53D17 37J05 37J35 PDFBibTeX XMLCite \textit{P. Foth}, J. Math. Phys. 43, No. 6, 3124--3132 (2002; Zbl 1059.53065) Full Text: DOI
Zakharevich, Ilya Kronecker webs, bihamiltonian structures, and the method of argument translation. (English) Zbl 0994.37034 Transform. Groups 6, No. 3, 267-300 (2001). Reviewer: Paulo R.Rodrigues (Rio de Janeiro) MSC: 37K10 37J35 53A60 37K30 PDFBibTeX XMLCite \textit{I. Zakharevich}, Transform. Groups 6, No. 3, 267--300 (2001; Zbl 0994.37034) Full Text: DOI arXiv
Faybusovich, Leonid; Gekhtman, Michael Poisson brackets on rational functions and multi-Hamiltonian structure for integrable lattices. (English) Zbl 1115.37336 Phys. Lett., A 272, No. 4, 236-244 (2000). MSC: 37J35 37K60 53D17 70H06 PDFBibTeX XMLCite \textit{L. Faybusovich} and \textit{M. Gekhtman}, Phys. Lett., A 272, No. 4, 236--244 (2000; Zbl 1115.37336) Full Text: DOI arXiv
Grigor’ev, M. A.; Semikhatov, A. M. A Kähler structure of the triplectic geometry. (English. Russian original) Zbl 1036.53051 Theor. Math. Phys. 124, No. 3, 1157-1171 (2000); translation from Teor. Mat. Fiz. 124, No. 3, 355-372 (2000). Reviewer: Oscar J. Garay (Bilbao) MSC: 53C55 53C80 58A50 81T60 PDFBibTeX XMLCite \textit{M. A. Grigor'ev} and \textit{A. M. Semikhatov}, Theor. Math. Phys. 124, No. 3, 1157--1171 (2000; Zbl 1036.53051); translation from Teor. Mat. Fiz. 124, No. 3, 355--372 (2000) Full Text: DOI arXiv