“Many-poled” r-matrix Lie algebras, Lax operators, and integrable systems

DOI10.1063/1.4891488zbMath1304.37050OpenAlexW2094889629MaRDI QIDQ3189961

T. V. Skrypnik

Publication date: 12 September 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.4891488

zbMATH Keywords

generalized classical Yang-Baxter equationLie-algebra-valued meromorphic functionsnon-skew-symmetric \(r\)-matrix

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Infinite-dimensional Lie (super)algebras (17B65) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) 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)

Symmetric separation of variables for trigonometric integrable models ⋮ On the general solution of the permuted classical Yang–Baxter equation and quasigraded Lie algebras ⋮ Anisotropic Z n-graded classical r-matrix, deformed A n Toda- and Gaudin-type models, and separation of variables ⋮ Reduction in soliton hierarchies and special points of classical \(r\)-matrices ⋮ Reductions in finite-dimensional integrable systems and special points of classical r-matrices ⋮ Separation of variables, quasi-trigonometric \(r\)-matrices and generalized Gaudin models ⋮ Separation of variables, Lax-integrable systems and \(gl(2) \otimes gl(2)\)-valued classical \(r\)-matrices

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