A trick loop algebra and a corresponding Liouville integrable hierarchy of evolution equations

DOI10.1016/j.chaos.2003.12.018zbMath1048.37064OpenAlexW2058182954MaRDI QIDQ1878209

Xi-Xiang Xu, Yu-Feng Zhang

Publication date: 19 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.chaos.2003.12.018

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Applications of Lie algebras and superalgebras to integrable systems (17B80) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

Related Items (1)

A hierarchy of discrete integrable coupling system with self-consistent sources

Cites Work

• Integrable theory of the perturbation equations.
• Integrable couplings of Botie-Pempinelli-Tu (BPT) hierarchy
• The bi-Hamiltonian structure of the perturbation equations of the KdV hierarchy.
• Integrable evolution systems based on Gerdjikov–Ivanov equations, bi-Hamiltonian structure, finite-dimensional integrable systems and N-fold Darboux transformation
• The Modified Korteweg-de Vries Equation
• Lie–Bäcklund symmetries of certain nonlinear evolution equations under perturbation around their solutions
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• A simple model of the integrable Hamiltonian equation
• Finite Dimensional Hamiltonians and Almost-Periodic Solutions for 2+1 Dimensional Three-Wave Equations
• A direct method for integrable couplings of TD hierarchy
• A powerful approach to generate new integrable systems
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