A general approach for getting the commutator representations of the hierarchies of nonlinear evolution equations

DOI10.1016/0375-9601(94)90036-1zbMath0961.37516OpenAlexW2029101927MaRDI QIDQ1341660

Zhijun Qiao

Publication date: 8 January 1995

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0375-9601(94)90036-1

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Ergodic theorems, spectral theory, Markov operators (37A30) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (16)

Two kinds of new integrable couplings of the negative-order Korteweg-de Vries equation ⋮ Wave solutions to an integrable negative order KdV equation ⋮ Soliton dynamics to the multi-component complex coupled integrable dispersionless equation ⋮ \((2+1)\)-dimensional local and nonlocal reductions of the negative AKNS system: soliton solutions ⋮ Algebro-geometric solutions of the sine-Gordon hierarchy ⋮ Algebraic structure of the operator related to stationary systems ⋮ A (2+1)-dimensional sine-Gordon and sinh-Gordon equations with symmetries and kink wave solutions ⋮ AN ALGEBRAIC STRUCTURE OF ZERO CURVATURE REPRESENTATIONS ASSOCIATED WITH COUPLED INTEGRABLE COUPLINGS AND APPLICATIONS TO τ-SYMMETRY ALGEBRAS ⋮ On \((2+1)\)-dimensional mixed AKNS hierarchy ⋮ Surfaces specified by integrable systems of partial differential equations determined by structure equations and Lax pair ⋮ Higher-order rational solitons and rogue-like wave solutions of the \((2+1)\)-dimensional nonlinear fluid mechanics equations ⋮ New Bäcklund transformations of the \((2+1)\)-dimensional Bogoyavlenskii equation via localization of residual symmetries ⋮ Generalized negative flows in hierarchies of integrable evolution equations ⋮ The quasi-periodic solutions of mixed KdV equations ⋮ Zero curvature representation, bi-Hamiltonian structure, and an integrable hierarchy for the Zakharov-Ito system ⋮ Integrable hierarchies related to the Kuper-CH spectral problem

Cites Work

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• On the use of isospectral eigenvalue problems for obtaining hereditary symmetries for Hamiltonian systems
• A nonconfocal generator of involutive systems and three associated soliton hierarchies
• The inverse scattering transform: Semi-infinite interval
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Method for Solving the Korteweg-deVries Equation
• On the Toda Lattice. II: Inverse-Scattering Solution

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