Adler–Kostant–Symes construction, bi-Hamiltonian manifolds, and KdV equations

DOI10.1063/1.531935zbMath0894.58024OpenAlexW1976393648MaRDI QIDQ4379257

Partha Guha

Publication date: 7 September 1998

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

Full work available at URL: https://doi.org/10.1063/1.531935

zbMATH Keywords

KdV equationbi-Hamiltonian manifoldsAdler-Kostant-Symes theoryFordy-Kulish scheme

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items (5)

THE τ FUNCTIONS OF THE AKS HIERARCHY AND TWISTOR CORRESPONDENCE ⋮ Hierarchies and Hamiltonian structures of the nonlinear Schrödinger family using geometric and spectral techniques ⋮ AKS hierarchy and bi-Hamiltonian geometry of Gelfand–Zakharevich type ⋮ Nonlinear bi-Hamiltonian dynamical systems: current Lie algebraic approach ⋮ Quest for Universal Integrable Models

Cites Work

• What is a classical r-matrix?
• Nonlinear Schrödinger equations and simple Lie algebras
• Lie algebras and equations of Korteweg-de Vries type
• Completely integrable systems, Euclidean Lie algebras, and curves
• Systems of Toda type, inverse spectral problems, and representation theory
• Drinfeld-Sokolov reduction on a simple Lie algebra from the bihamiltonian point of view
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• Reduction of Hamiltonian systems, affine Lie algebras and Lax equations
• A self-dual Yang-Mills hierarchy and its reductions to integrable systems in \(1+1\) and \(2+1\) dimensions
• On commuting flows of AKS hierarchy and twistor correspondence
• A loop algebra co-adjoint orbit construction of the generalized KdV hierarchies
• ON SYMPLECTIC STRUCTURES AND INTEGRABLE SYSTEMS ON SYMMETRIC SPACES
• A simple model of the integrable Hamiltonian equation
• On the Virasoro Algebra as Reduced Poisson Submanifold of a Kac-Moody Algebra on the Circle

This page was built for publication: Adler–Kostant–Symes construction, bi-Hamiltonian manifolds, and KdV equations