Bi-integrable couplings of a Kaup-Newell type soliton hierarchy and their bi-Hamiltonian structures

DOI10.1016/j.cnsns.2014.12.008zbMath1351.37253OpenAlexW2091389715MaRDI QIDQ727096

Shui Meng Yu, Shou-feng Shen, Yu-Qin Yao, Wen-Xiu Ma

Publication date: 6 December 2016

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2014.12.008

zbMATH Keywords

Hamiltonian structureLiouville integrabilitymatrix spectral problemintegrable couplingKaup-Newell type soliton hierarchy

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10)

Related Items (4)

N-fold Darboux Transformation for Integrable Couplings of AKNS Equations ⋮ The bi-integrable couplings of two-component Casimir-Qiao-Liu type hierarchy and their Hamiltonian structures ⋮ Hamiltonian model and dynamic analyses for a hydro-turbine governing system with fractional item and time-lag ⋮ Bi-integrable couplings associated with \(\mathrm{so}(3,\mathbb{R})\)

Cites Work

• Unnamed Item
• Nonlinear continuous integrable Hamiltonian couplings
• Constructing nonlinear discrete integrable Hamiltonian couplings
• A Hamiltonian structure associated with a matrix spectral problem of arbitrary-order
• A hierarchy of non-isospectral multi-component AKNS equations and its integrable couplings
• Integrable theory of the perturbation equations.
• A soliton hierarchy associated with \(\mathrm{so}(3,\mathbb R)\)
• Semi-direct sums of Lie algebras and continuous integrable couplings
• The algebraic structure of discrete zero curvature equations associated with integrable couplings and application to enlarged Volterra systems
• Coupled KdV equations with multi-Hamiltonian structures
• A generalized Wadati--Konno--Ichikawa hierarchy and its binary nonlinearization by symmetry constraints.
• A generalized Wadati-Konno-Ichikawa hierarchy and new finite-dimensional integrable systems
• The multi-component generalized Wadati-Konono-Ichikawa (WKI) hierarchy and its multi-component integrable couplings system with two arbitrary functions
• Adjoint symmetry constraints of multicomponent AKNS equations.
• The bi-Hamiltonian structure of the perturbation equations of the KdV hierarchy.
• The Nonlinear Evolution Equations Related to the Wadati-Konno-Ichikawa Spectral Problem
• New Integrable Nonlinear Evolution Equations
• An integrable system and associated integrable models as well as Hamiltonian structures
• Integrable couplings of vector AKNS soliton equations
• COUPLING INTEGRABLE COUPLINGS
• Component-trace identities for Hamiltonian structures
• THE ALGEBRAIC STRUCTURE OF ZERO CURVATURE REPRESENTATIONS ASSOCIATED WITH INTEGRABLE COUPLINGS
• Coupled Harry Dym equations with multi-Hamiltonian structures
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• A trace identity and its application to integrable systems of 1 + 2 dimensions
• An exact solution for a derivative nonlinear Schrödinger equation
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• A coupled AKNS–Kaup–Newell soliton hierarchy
• AN ALGEBRAIC STRUCTURE OF ZERO CURVATURE REPRESENTATIONS ASSOCIATED WITH COUPLED INTEGRABLE COUPLINGS AND APPLICATIONS TO τ-SYMMETRY ALGEBRAS
• Four Lie algebras associated with R6 and their applications
• Three kinds of coupling integrable couplings of the Korteweg–de Vries hierarchy of evolution equations
• Coupling integrable couplings and bi-Hamiltonian structure associated with the Boiti–Pempinelli–Tu hierarchy
• Lie algebras and Hamiltonian structures of multi-component Ablowitz–Kaup–Newell–Segur hierarchy
• A spectral problem based on so$(3,\mathbb {R})$(3,R) and its associated commuting soliton equations
• 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
• A trace identity and its applications to the theory of discrete 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: Bi-integrable couplings of a Kaup-Newell type soliton hierarchy and their bi-Hamiltonian structures