Hierarchies of finite-dimensional Lax equations with a spectral parameter on a Riemann surface and semisimple Lie algebras

DOI10.1007/s11232-015-0381-0zbMath1417.37246OpenAlexW2279941765MaRDI QIDQ269040

Oleg K. Sheinman

Publication date: 18 April 2016

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11232-015-0381-0

zbMATH Keywords

Riemann surfacehierarchyLax equationsemisimple Lie algebraLax operator algebra

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relationships between algebraic curves and integrable systems (14H70) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Applications of Lie algebras and superalgebras to integrable systems (17B80) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

Related Items (7)

Matrix divisors on Riemann surfaces and Lax operator algebras ⋮ Spectral curves of the hyperelliptic Hitchin systems ⋮ Semisimple Lie algebras and Hamiltonian theory of finite-dimensional Lax equations with spectral parameter on a Riemann surface ⋮ Hitchin systems on hyperelliptic curves ⋮ Polynomial dynamical systems and the Korteweg-de Vries equation ⋮ Certain reductions of Hitchin systems of rank 2 and genera 2 and 3 ⋮ Hirzebruch functional equation: classification of solutions

Cites Work

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• HOLOMORPHIC BUNDLES OVER ALGEBRAIC CURVES AND NON-LINEAR EQUATIONS
• Central extensions of Lax operator algebras
• Classification of vector bundles over an algebraic curve of arbitrary genus

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