{"title":"INTEGRATION OF THE NONLINEAR SCHR\\\"{O}DINGER EQUATION WITH A SELF-CONSISTENT SOURCE AND NONZERO BOUNDARY CONDITIONS","authors":"A. Reyimberganov","doi":"10.12732/ijam.v36i3.4","DOIUrl":null,"url":null,"abstract":"This paper is devoted to the study of the defocusing nonlinear Schr\\\"{o}dinger equation with a self-consistent source and nonzero boundary conditions by the method of the inverse scattering problem. In cases where the source consists of a combination of eigenfunctions of the corresponding spectral problem for the Zakharov-Shabat system, the complete integrability of the nonlinear Schr\\\"{o}dinger equation is investigated. Namely, the evolutions of the scattering data of the self-adjoint Zakharov-Shabat system, whose potential is a solution of the defocusing nonlinear Schr\\\"{o}dinger equation with a self-consistent source, are obtained.","PeriodicalId":37513,"journal":{"name":"International Journal of Applied Mathematics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12732/ijam.v36i3.4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is devoted to the study of the defocusing nonlinear Schr\"{o}dinger equation with a self-consistent source and nonzero boundary conditions by the method of the inverse scattering problem. In cases where the source consists of a combination of eigenfunctions of the corresponding spectral problem for the Zakharov-Shabat system, the complete integrability of the nonlinear Schr\"{o}dinger equation is investigated. Namely, the evolutions of the scattering data of the self-adjoint Zakharov-Shabat system, whose potential is a solution of the defocusing nonlinear Schr\"{o}dinger equation with a self-consistent source, are obtained.
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The journal is peer-reviewed and publishes carefully selected original research papers on all scopes of mathematics and its applications: combinatorics, design and configurations, graph theory, fractals, lattices, ordered algebraic structures, real functions, measure and integration, functions of complex variable, potential theory, special functions, fractional calculus, operational calculus and integral transforms, dynamical systems in their broadest sense (covering ODEs, all kinds of PDEs, FDEs, difference equations, functional equations), approximation and expansion, integral equations, operator theory, calculus of variations, optimal control, optimization, applied differential geometry, probability theory and stochastic processes, statistics, numerical analysis, computer science, mechanics of particle and systems, mechanics of solids, fluid mechanics, classical thermodynamics, mathematical methods in economics, operations research, programming, mathematical biology, systems theory, information and communication, circuits.
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