Modified non-Abelian Toda field equations and twisted quasigraded Lie algebras

DOI10.1063/1.2207719zbMath1112.37073OpenAlexW2062477958MaRDI QIDQ3441938

T. V. Skrypnik

Publication date: 16 May 2007

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

Full work available at URL: https://doi.org/10.1063/1.2207719

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Groups and algebras in quantum theory and relations with integrable systems (81R12) Lattice dynamics; integrable lattice equations (37K60) Lie algebras and Lie superalgebras (17Bxx)

Related Items (6)

Quantum integrable systems, non-skew-symmetric r-matrices and algebraic Bethe ansatz ⋮ Reduction in soliton hierarchies and special points of classical \(r\)-matrices ⋮ Separation of variables for quadratic algebras: Algebras of Maillet and reflection-equation algebras ⋮ Twisted rational \(r\)-matrices and algebraic Bethe ansatz: application to generalized Gaudin and Richardson models ⋮ Anisotropic BCS-Richardson model and algebraic Bethe ansatz ⋮ Quasigraded bases in loop algebras and classical rational r-matrices

Cites Work

• Kac-Moody Lie algebras and soliton equations. III: Stationary equations associated with \(A_ 1^{(1)}\)
• Generalized Drinfel'd-Sokolov hierarchies
• Quasigraded deformations of loop algebras and classical integrable systems.
• To a transformation theory of two-dimensional integrable systems
• Quasigraded Lie algebras on hyperelliptic curves and classical integrable systems
• Deformations of loop algebras and integrable systems: hierarchies of integrable equations
• Doubled  generalized Landau–Lifshitz hierarchies and special quasigraded Lie algebras
• The n-component KP hierarchy and representation theory

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