Application of a semi-direct sum of Lie algebras to the TD hierarchy

DOI10.1016/j.chaos.2008.10.009zbMath1198.37101OpenAlexW2087964430MaRDI QIDQ602633

Fucai You, Tie-cheng Xia

Publication date: 5 November 2010

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

Full work available at URL: https://doi.org/10.1016/j.chaos.2008.10.009

Mathematics Subject Classification ID

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

Cites Work

• Unnamed Item
• Integrable theory of the perturbation equations.
• A new loop algebra \(\tilde A_5\) and its applications to integrable system
• Semi-direct sums of Lie algebras and continuous integrable couplings
• Enlarging spectral problems to construct integrable couplings of soliton equations
• A generalized AKNS hierarchy and its bi-Hamiltonian structures
• Integrable couplings of the generalized AKNS hierarchy with an arbitrary function and its bi-Hamiltonian structure
• The integrable couplings of the generalized coupled Burgers hierarchy and its Hamiltonian structures
• A generalized MKdV hierarchy, tri-Hamiltonian structure, higher-order binary constrained flows and its integrable couplings system
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• A simple model of the integrable Hamiltonian equation
• Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras
• The quadratic-form identity for constructing the Hamiltonian structure of integrable systems