Abstract:
The Hamiltonian property and integrability of the Lax equations with spectral parameter on a Riemann surface are considered. The operators of Lax pairs are meromorphic functions of special form on a Riemann surface of arbitrary positive genus with values in an arbitrary semisimple Lie algebra. The study combines the theory of Lax equations with spectral parameter on a Riemann surface, as proposed by I.M. Krichever in 2001, with a “group-theoretic approach.”
Citation:
O. K. Sheinman, “Semisimple Lie algebras and Hamiltonian theory of finite-dimensional Lax equations with spectral parameter on a Riemann surface”, Modern problems of mathematics, mechanics, and mathematical physics, Collected papers, Trudy Mat. Inst. Steklova, 290, MAIK Nauka/Interperiodica, Moscow, 2015, 191–201; Proc. Steklov Inst. Math., 290:1 (2015), 178–188
This publication is cited in the following 8 articles:
Juan Yue, Zhonglong Zhao, Abdul-Majid Wazwaz, “Solitons, nonlinear wave transitions and characteristics of quasi-periodic waves for a (3+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation in fluid mechanics and plasma physics”, Chinese Journal of Physics, 89 (2024), 896
O. K. Sheinman, “Certain reductions of Hitchin systems of rank 2 and genera 2 and 3”, Dokl. Math., 97:2 (2018), 144–146
Elena Yu. Bunkova, “Hirzebruch functional equation: classification of solutions”, Proc. Steklov Inst. Math., 302 (2018), 33–47
O. K. Sheinman, “Matrix divisors on Riemann surfaces and Lax operator algebras”, Trans. Moscow Math. Soc., 78 (2017), 109–121
O. K. Sheinman, “Lax operator algebras and integrable systems”, Russian Math. Surveys, 71:1 (2016), 109–156
V. M. Buchstaber, “Polynomial dynamical systems and the Korteweg–de Vries equation”, Proc. Steklov Inst. Math., 294 (2016), 176–200
O. K. Sheinman, “Ispravlenie k rabote “Poluprostye algebry Li i gamiltonova teoriya konechnomernykh uravnenii Laksa so spektralnym parametrom na rimanovoi poverkhnosti” (Tr. MIAN. 2015. T. 290. S. 191–201)”, Sovremennye problemy matematiki, mekhaniki i matematicheskoi fiziki. II, Sbornik statei, Trudy MIAN, 294, MAIK «Nauka/Interperiodika», M., 2016, 325–327
Oleg K. Sheinman, “Global current algebras and localization on Riemann surfaces”, Mosc. Math. J., 15:4 (2015), 833–846
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