Binary nonlinearization of spectral problems of the perturbation AKNS systems.

DOI10.1016/S0960-0779(01)00152-7zbMath1067.37097OpenAlexW2012887527MaRDI QIDQ1610083

Ruguang Zhou, Wen-Xiu Ma

Publication date: 18 August 2002

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

Full work available at URL: https://doi.org/10.1016/s0960-0779(01)00152-7

zbMATH Keywords

perturbationAKNS hierarchyfinite-dimensional Hamiltonian systems

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

Related Items (9)

A new integrable hierarchy and constrained flows, its expanding integrable system ⋮ The binary nonlinearization of the super integrable system and its self-consistent sources ⋮ Adjoint symmetry constraints of the vector KN equations and their integrable coupling system ⋮ Constructing \((2+1)\)-dimensional nonlinear soliton equations with a generalized zero curvature equation ⋮ A new \(4\times 4\) AKNS spectral problem and its associated integrable decomposition of the AKNS equation ⋮ Semi-direct sums of Lie algebras and continuous integrable couplings ⋮ The Liouville integrability of integrable couplings of Volterra lattice equation ⋮ Hierarchies, integrable decompositions and conservation laws of Geng equation ⋮ Two kinds of new integrable decompositions of the Gerdjikov-Ivanov equation

Cites Work

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• Nonlinearization of the Lax system for AKNS hierarchy
• Integrable theory of the perturbation equations.
• Binary nonlinearization of AKNS spectral problem under higher-order symmetry constraints.
• The bi-Hamiltonian structure of the perturbation equations of the KdV hierarchy.
• On the complete integrability of nonlinearized Lax systems for the classical Boussinesq hierachy
• Algebro-geometric solutions of (2+1)-dimensional coupled modified Kadomtsev–Petviashvili equations
• A finite-dimensional integrable system and the r-matrix method
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• Restricted flows of soliton hierarchies: coupled KdV and Harry Dym case
• Restricted flows of the AKNS hierarchy
• Relation between the Kadometsev–Petviashvili equation and the confocal involutive system
• A hierarchy of nonlinear evolution equations and finite-dimensional involutive systems
• The finite-band solution of the Jaulent–Miodek equation
• Classical Poisson structures andr-matrices from constrained flows
• New Finite-Dimensional Integrable Systems by Symmetry Constraint of the KdV Equations
• DerivingN-soliton solutions via constrained flows
• An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems
• Nonlinearization of spectral problems for the perturbation KdV systems
• Integrable couplings of soliton equations by perturbations. I: A general theory and application to the KdV hierarchy

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