Completion of the Ablowitz-Kaup-Newell-Segur integrable coupling

DOI10.1063/1.4990534zbMath1404.37084arXiv1706.04308OpenAlexW3106012793MaRDI QIDQ4556645

Wen-Xiu Ma, Yongyang Jin, Shou-feng Shen, Chun-Xia Li

Publication date: 16 November 2018

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

Full work available at URL: https://arxiv.org/abs/1706.04308

zbMATH Keywords

bi-Hamiltonian structurenon-semisimple Lie algebras

Mathematics Subject Classification ID

Related Items (10)

Completion of the Guo-Hierarchy Integrable Coupling with Self-Consistent Sources in a Nonlinear Wave System ⋮ A novel kind of a multicomponent hierarchy of discrete soliton equations and its application ⋮ Integrable asymmetric AKNS model with multi-component ⋮ Unnamed Item ⋮ A kind of generalized integrable couplings and their bi-Hamiltonian structure ⋮ Explicit solutions to a coupled integrable lattice equation ⋮ A kind of nonisospectral and isospectral integrable couplings and their Hamiltonian systems ⋮ \( \bar\partial \)-dressing method for a few \((2+1)\)-dimensional integrable coupling systems ⋮ A new multi-component integrable coupling and its application to isospectral and nonisospectral problems ⋮ Application of Riemann-Hilbert method to an extended coupled nonlinear Schrödinger equations

Cites Work

• Unnamed Item
• Variational identities and applications to Hamiltonian structures of soliton equations
• Nonlinear continuous integrable Hamiltonian couplings
• Two unified formulae
• Constructing nonlinear discrete integrable Hamiltonian couplings
• A hierarchy of non-isospectral multi-component AKNS equations and its integrable couplings
• Integrable theory of the perturbation equations.
• The computational formula on the constant \(\gamma\) appeared in the equivalently used trace identity and quadratic-form identity
• 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
• New simple method for obtaining integrable hierarchies of soliton equations with multicomponent potential functions
• The multi-component generalized Wadati-Konono-Ichikawa (WKI) hierarchy and its multi-component integrable couplings system with two arbitrary functions
• A generalized multi-component Glachette-Johnson (GJ) hierarchy and its integrable coupling system
• The integrable coupling of the AKNS hierarchy and its Hamiltonian structure
• Multi-component integrable couplings for the Ablowitz-Kaup-Newell-Segur and Volterra hierarchies
• 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 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
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• A new loop algebra and a corresponding integrable hierarchy, as well as its integrable coupling
• 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
• 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

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