A Lax integrable hierarchy, bi-Hamiltonian structure and finite-dimensional Liouville integrable involutive systems

DOI10.1016/J.CHAOS.2004.03.011zbMath1060.37062OpenAlexW2046583501MaRDI QIDQ1766615

Xiaohong Chen, Tie-cheng Xia, Deng-Yuan Chen

Publication date: 8 March 2005

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2004.03.011

zbMATH Keywords

eigenvalue problemintegrabilityinvolutive solutionsnonlinear evolution equationsgeneralized nonlinear Schrödinger equationsgeneralized mKdV equations

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) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (9)

A Liouville integrable hierarchy, symmetry constraint, new finite-dimensional integrable systems, involutive solution and expanding integrable models ⋮ TWO FAMILIES GENERALIZATION OF AKNS HIERARCHIES AND THEIR HAMILTONIAN STRUCTURES ⋮ The multicomponent generalized Kaup–Newell hierarchy and its multicomponent integrable couplings system with two arbitrary functions ⋮ The multi-component TA hierarchy and its multi-component integrable couplings system with six arbitrary functions ⋮ A generalized AKNS hierarchy and its bi-Hamiltonian structures ⋮ The multi-component generalized Wadati-Konono-Ichikawa (WKI) hierarchy and its multi-component integrable couplings system with two arbitrary functions ⋮ The multi-component Yang hierarchy and its multi-component integrable coupling system with two arbitrary functions ⋮ Two types of new Lie algebras and corresponding hierarchies of evolution equations ⋮ A generalized cubic Volterra lattice hierarchy and its integrable couplings system

Cites Work

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• Integrable theory of the perturbation equations.
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• Bi-Hamiltonian structure of modified Volterra model
• Applications of an anti-symmetry loop algebra and its expanding forms
• Integrable systems of derivative nonlinear Schrödinger type and their multi-Hamiltonian structure
• Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws
• The Modified Korteweg-de Vries Equation
• Finite-dimensional discrete systems and integrable systems through nonlinearization of the discrete eigenvalue problem
• A coupled AKNS–Kaup–Newell soliton hierarchy
• A Bargmann system and the involutive representation of solutions of the Levi hierarchy
• Classical Poisson structures andr-matrices from constrained flows

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