The multicomponent generalized Kaup–Newell hierarchy and its multicomponent integrable couplings system with two arbitrary functions

DOI10.1063/1.1866220zbMath1067.37103OpenAlexW2048702978MaRDI QIDQ3024327

Tie-cheng Xia, En-gui Fan

Publication date: 30 June 2005

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.1866220

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) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items

Multi-component generalized Gerdjikov-Ivanov integrable hierarchy and its Riemann-Hilbert problem ⋮ General soliton solutions to a coupled Fokas-Lenells equation ⋮ Upper Triangular Matrix of Lie Algebra and a New Discrete Integrable Coupling System ⋮ A generalized AKNS hierarchy, bi-Hamiltonian structure, and Darboux transformation ⋮ Hierarchies of multi-component mKP equations and theirs integrable couplings ⋮ Conservation laws, bright matter wave solitons and modulational instability of nonlinear Schrödinger equation with time-dependent nonlinearity ⋮ INTEGRABLE COUPLINGS OF MULTI-COMPONENT AKNS–KAUP–NEWELL EQUATIONS HIERARCHIES ⋮ AN ALGEBRAIC STRUCTURE OF ZERO CURVATURE REPRESENTATIONS ASSOCIATED WITH COUPLED INTEGRABLE COUPLINGS AND APPLICATIONS TO τ-SYMMETRY ALGEBRAS ⋮ INTEGRABLE COUPLINGS OF SUPER KAUP–NEWELL EQUATION HIERARCHY ⋮ Integrable decomposition of a hierarchy of soliton equations and integrable coupling system by semidirect sums of Lie algebras ⋮ A new \(4\times 4\) AKNS spectral problem and its associated integrable decomposition of the AKNS equation ⋮ Two hierarchies of multi-component Kaup-Newell equations and theirs integrable couplings ⋮ Multi-component bi-Hamiltonian Dirac integrable equations ⋮ THE ALGEBRAIC STRUCTURE OF ZERO CURVATURE REPRESENTATIONS ASSOCIATED WITH INTEGRABLE COUPLINGS ⋮ Two types of new Lie algebras and related Liouville integrable hierarchies ⋮ Hierarchies, integrable decompositions and conservation laws of Geng equation ⋮ Dynamic behaviors of mixed localized solutions for the three-component coupled Fokas-Lenells system ⋮ The algebraic structure of discrete zero curvature equations associated with integrable couplings and application to enlarged Volterra systems ⋮ A generalized coupled Korteweg–de Vries hierarchy, bi-Hamiltonian structure, and Darboux transformation ⋮ Soliton solution of a multi-component higher-order Ito equation

Cites Work

• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems. II
• A Lax integrable hierarchy, bi-Hamiltonian structure and finite-dimensional Liouville integrable involutive systems
• Variable separation and algebro-geometric solutions of the Gerdjikov-Ivanov equation
• A new Lax integrable hierarchy, \(N\) Hamiltonian structure and its integrable couplings system
• Adjoint symmetry constraints of multicomponent AKNS equations.
• A generalized multi-component Glachette-Johnson (GJ) hierarchy and its integrable coupling system
• New integrable systems of derivative nonlinear Schrödinger equations with multiple components
• Integrable systems of derivative nonlinear Schrödinger type and their multi-Hamiltonian structure
• Integrable evolution systems based on Gerdjikov–Ivanov equations, bi-Hamiltonian structure, finite-dimensional integrable systems and N-fold Darboux transformation
• Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws
• The Modified Korteweg-de Vries Equation
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• Hamiltonian structure of discrete soliton systems
• Multi-Field Integrable Systems Related to WKI-Type Eigenvalue Problems
• A new loop algebra and a corresponding integrable hierarchy, as well as its integrable coupling
• Integrable Couplings of the Coupled Burgers Hierarchy
• Multi-component C-KdV Hierarchy of Soliton Equations and Its Multi-component Integrable Coupling System
• A Liouville integrable Hamiltonian system associated with a generalized Kaup-Newell spectral problem