Algebraic representation of the linear problem as a method to construct the Darboux-Bäcklund transformation.

DOI10.1016/0960-0779(94)E0100-4zbMath1080.37588OpenAlexW2171157664MaRDI QIDQ812267

Jan L. Cieśliński

Publication date: 16 February 2006

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

Full work available at URL: https://doi.org/10.1016/0960-0779(94)e0100-4

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) Geometric theory, characteristics, transformations in context of PDEs (35A30) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (5)

The Darboux-Bianchi transformation for isothermic surfaces. Classical results versus the soliton approach ⋮ Darboux transformation of the coupled nonisospectral Gross-Pitaevskii system and its multi-component generalization ⋮ Darboux transformation for the non-isospectral AKNS hierarchy and its asymptotic property ⋮ Darboux transformation for the nonisospectral AKNS system ⋮ Darboux-Bäcklund Transformations for Spin-Valued Linear Problems

Cites Work

• The reduction problem and the inverse scattering method
• Inverse scattering method with variable spectral parameter
• A hierarchy of coupled Korteweg-de Vries equations and the normalisation conditions of the Hilbert-Riemann problem
• An exact solution for a derivative nonlinear Schrödinger equation
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