A new Lie algebra and soliton solutions, Bäcklund transformation of soliton equations

DOI10.1016/j.chaos.2009.03.062zbMath1198.37100OpenAlexW1980140874WikidataQ115359295 ScholiaQ115359295MaRDI QIDQ603778

Yu-Feng Zhang, Hon-Wah Tam

Publication date: 8 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.2009.03.062

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) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (1)

The quasi-AKNS and quasi-\(s o(3)\) type AKNS hierarchies as well as a gallery of simple Lie algebras contained in \(s l(3; \mathbb{C})\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Integrable theory of the perturbation equations.
• Semi-direct sums of Lie algebras and continuous integrable couplings
• A new involutive system of polynomials and its classical integrable systems
• A hierarchy of Liouville integrable finite-dimensional Hamiltonian systems
• A generalized Boite-Pempinelli-Tu (BPT) hierarchy and its bi-Hamiltonian structure
• Integrable couplings of the hierarchies of evolution equations.
• Conte truncated expansion and applications
• An integrable Hamiltonian hierarchy and its constrained flows with generalized Hamiltonian regular representations, as well as its expanding integrable system
• An approach for constructing loop algebra via exterior algebra and its applications
• A new algebraic system and its applications
• A generalized multi-component Glachette-Johnson (GJ) hierarchy and its integrable coupling system
• Hamiltonian structure of the integrable coupling of the Jaulent-Miodek hierarchy
• Solitary wave solutions for variant Boussinesq equations
• New integrable couplings and Hamiltonian structure of the KN hierarchy and the DLW hierarchy
• A few subalgebras of the Lie algebra \(A_{3}\) and a direct approach for obtaining integrable couplings
• Vector loop algebra and its applications to integrable system
• A new Lie algebra, a corresponding multi-component integrable hierarchy and an integrable coupling
• A Generalization of Inverse Scattering Method
• New Integrable Nonlinear Evolution Equations
• ON INTEGRABLE COUPLINGS OF THE DISPERSIVE LONG WAVE HIERARCHY AND THEIR HAMILTONIAN STRUCTURE
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• The inverse scattering transform: Semi-infinite interval
• A hierarchy of coupled Burgers systems possessing a hereditary structure
• A direct method for integrable couplings of TD hierarchy
• A new loop algebra and a corresponding integrable hierarchy, as well as its integrable coupling
• 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
• Integrable couplings of soliton equations by perturbations. I: A general theory and application to the KdV hierarchy

This page was built for publication: A new Lie algebra and soliton solutions, Bäcklund transformation of soliton equations