An approach for constructing loop algebra via exterior algebra and its applications

DOI10.1016/J.CHAOS.2004.05.007zbMath1088.37037OpenAlexW2067918542MaRDI QIDQ1771632

Hon-Wah Tam, Yu-Feng Zhang

Publication date: 18 April 2005

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

Full work available at URL: https://doi.org/10.1016/j.chaos.2004.05.007

zbMATH Keywords

Burgers equationAKNS hierarchyheat-conduction equationKN hierarchymulti-component matrix loop algebra

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) Heat equation (35K05) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

Related Items (7)

A new integrable hierarchy and constrained flows, its expanding integrable system ⋮ A new Lie algebra and soliton solutions, Bäcklund transformation of soliton equations ⋮ An unified form of the AKNS and BPT hierarchies with two arbitrary parameters ⋮ Constructing \((2+1)\)-dimensional nonlinear soliton equations with a generalized zero curvature equation ⋮ A new loop algebra and its application to the multi-component S-mKdV hierarchy ⋮ INTEGRABLE HAMILTONIAN HIERARCHIES ASSOCIATED WITH THE EQUATION OF HEAT CONDUCTION ⋮ GENERALIZED mKdV EQUATION, LIOUVILLE EQUATION, SINE-GORDON EQUATION AND SINH-GORDON EQUATION AS WELL AS A FORMAL BÄCKLUND TRANSFORMATION

Cites Work

• The Coupled Modified Korteweg-de Vries Equations
• Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws
• The Modified Korteweg-de Vries Equation
• New Integrable Nonlinear Evolution Equations
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• The inverse scattering transform: Semi-infinite interval
• Multi-Field Integrable Systems Related to WKI-Type Eigenvalue Problems
• Lax Pairs for Four-Wave Interaction Systems
• A new loop algebra and a corresponding integrable hierarchy, as well as its integrable coupling
• Unnamed Item

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