Classical r-matrices and compatible Poisson brackets for coupled KdV systems

DOI10.1007/BF00420010zbMath0699.58043MaRDI QIDQ913341

A. G. Reyman, Allan P. Fordy, Michaael A. Semenov-Tian-Shansky

Publication date: 1989

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

zbMATH Keywords

compatible Poisson brackets

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 Lie (super)algebras (17B65) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items (11)

An \(r\)-matrix interpretation of modified systems ⋮ Integrability of the Frobenius algebra-valued Kadomtsev-Petviashvili hierarchy ⋮ The R-matrix theory and the reduction of Poisson manifolds ⋮ Factorisation of energy dependent Schrödinger operators: Miura maps and modified systems ⋮ The Frobenius-Virasoro algebra and Euler equations ⋮ Quasiclassical limit of coupled KdV equations. Riemann invariants and multi-Hamiltonian structure ⋮ Singular sector of the Kadomtsev–Petviashvili hierarchy, ∂̄ operators of nonzero index, and associated integrable systems ⋮ A Lie algebraic setting for Miura maps related to an energy dependent linear problem ⋮ Hidden hierarchies of KdV type on Birkhoff strata ⋮ New integrable hierarchies from vertex operator representations of polynomial Lie algebras ⋮ On the Hamiltonian formalism for Korteweg-de Vries type hierarchies

Cites Work

• Factorisation of energy dependent Schrödinger operators: Miura maps and modified systems
• Coupled KdV equations with multi-Hamiltonian structures
• Coupled Harry Dym equations with multi-Hamiltonian structures

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