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Integrable semi-discretization of the coupled nonlinear Schr\"{o}dinger equations

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arxiv solv-int/9903013 v1 pith:5X75ELJC submitted 1999-03-18 solv-int nlin.SI

T. Tsuchida , H. Ujino , M. Wadati (University of Tokyo) This is my paper · ORCID
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keywords dingernonlinearschrcoupleddiscreteequationsextensioninverse
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A system of semi-discrete coupled nonlinear Schr\"{o}dinger equations is studied. To show the complete integrability of the model with multiple components, we extend the discrete version of the inverse scattering method for the single-component discrete nonlinear Schr\"{o}dinger equation proposed by Ablowitz and Ladik. By means of the extension, the initial-value problem of the model is solved. Further, the integrals of motion and the soliton solutions are constructed within the framework of the extension of the inverse scattering method.

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  1. Integrable Twelve-Component Nonlinear Dynamical System on a Quasi-One-Dimensional Lattice

    nlin.SI 2025-09 conditional novelty 6.0 of 10

    Two new semi-discrete multi-component integrable systems with explicit Lax pairs and local conservation laws are constructed on a quasi-one-dimensional lattice.

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