Lie algebraic structures of (1+1)-dimensional Lax integrable systems

DOI10.1063/1.531742zbMath0860.58021OpenAlexW2088613503MaRDI QIDQ4716470

Deng-Juan Chen, Da-jun Zhang

Publication date: 21 April 1997

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

Full work available at URL: https://doi.org/10.1063/1.531742

zbMATH Keywords

isospectral flowsAKNS systemLax integrable systemnonisospectral flows

Mathematics Subject Classification ID

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

Related Items (15)

Symmetries and their Lie algebra of a variable coefficient Korteweg-de Vries hierarchy ⋮ The exact solutions for a nonisospectral nonlinear Schrödinger equation ⋮ Darboux transformation and Hamiltonian structure for the Jaulent-Miodek hierarchy ⋮ Lie algebraic structures of some (1+2)-dimensional Lax integrable systems. ⋮ Soliton solutions to the nonlocal non-isospectral nonlinear Schrödinger equation ⋮ New symmetries for the Ablowitz-Ladik hierarchies ⋮ Lie algebras and Hamiltonian structures of multi-component Ablowitz–Kaup–Newell–Segur hierarchy ⋮ SYMMETRIES AND LIE ALGEBRA OF THE DIFFERENTIAL–DIFFERENCE KADOMSTEV–PETVIASHVILI HIERARCHY ⋮ \(N\)-soliton solutions and double Wronskian solution of the non-isospectral AKNS equation ⋮ New set of symmetries and Lie algebraic structures of the Toda lattice hierarchy ⋮ Soliton solutions, rational solutions, Matveev solutions, complexitons and mixed solutions for three (2+1)-dimension equations ⋮ Symmetries for the Ablowitz-Ladik Hierarchy: Part I. Four-Potential Case ⋮ Symmetries for the Ablowitz-Ladik Hierarchy: Part II. Integrable Discrete Nonlinear Schrödinger Equations and Discrete AKNS Hierarchy ⋮ THE MULTI-SOLITON SOLUTIONS FOR THE NON-ISOSPECTRAL mKdV–SINE-GORDON EQUATION ⋮ Hierarchy of lax integrable lattice equations, darboux transformation and conservation laws

Cites Work

• A note on Hamiltonian structure
• On the use of isospectral eigenvalue problems for obtaining hereditary symmetries for Hamiltonian systems
• Lax representations and Lax operator algebras of isospectral and nonisospectral hierarchies of evolution equations
• Lie algebraic structure for the AKNS system

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