R-MATRICES AND HAMILTONIAN STRUCTURES FOR CERTAIN LAX EQUATIONS

DOI10.1142/S0129055X13500050zbMath1315.37046arXiv1012.5245OpenAlexW2964261043MaRDI QIDQ5299776

Chao-Zhong Wu

Publication date: 21 June 2013

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

Full work available at URL: https://arxiv.org/abs/1012.5245

zbMATH Keywords

Hamiltonian structure\(R\)-matrixToda lattice hierarchytwo-component BKP hierarchy

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Applications of Lie algebras and superalgebras to integrable systems (17B80)

Related Items (6)

An extension of the Kadomtsev-Petviashvili hierarchy and its Hamiltonian structures ⋮ Hamiltonian structures of a coupled Ramani equation ⋮ On Lax equations of the two-component BKP hierarchy ⋮ From additional symmetries to linearization of Virasoro symmetries ⋮ Infinite-dimensional Frobenius manifolds underlying the Toda lattice hierarchy ⋮ Bilinear equation and additional symmetries for an extension of the Kadomtsev-Petviashvili hierarchy

Cites Work

• Infinite-dimensional Frobenius manifolds for \(2+1\) integrable systems
• The Hamiltonian structures of the two-dimensional Toda lattice and \(R\)-matrices
• Nonlinear Poisson structures and r-matrices
• Frobenius manifolds and central invariants for the Drinfeld-Sokolov bihamiltonian structures
• Transformation groups of soliton equations. IV: A new hierarchy of soliton equations of KP-type
• Transformation groups for soliton equations. Euclidean Lie algebras and reduction of the KP hierarchy
• Reduction of Poisson manifolds
• Integrable hierarchy underlying topological Landau-Ginzburg models of \(D\)-type
• Classical \(r\)-matrices and compatible Poisson structures for Lax equations on Poisson algebras
• The integrability of the 2-Toda lattice on \(\mathfrak{sl}_n (\mathbb{C})\) and its generalization to semi-simple Lie algebras
• R-matrices and higher Poisson brackets for integrable systems
• Bihamiltonian structure of the two-component Kadomtsev–Petviashvili hierarchy of type B
• The extended bigraded Toda hierarchy

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