On the solution of the nonlinear Schrödinger equation.
type: Item
instance of: scholarly article
title: On the solution of the nonlinear Schrödinger equation.
zbMATH Open document ID: 1055.35122
DOI: 10.1016/S0960-0779(02)00308-9
author: Hassan A. Zedan
author: Elsayed M. E. Zayed
published in: Chaos, Solitons and Fractals
publication date: 2004-01-14T00:00:00Z
review text: The authors consider the family of Schrödinger equations \[ iq_t+ q_{xx}+ q(| q|^2- S(x,t))= 0.\tag{1} \] In this paper, a complete classification with respect to the function \(S(x,t)\) is given by using the allowed transformation, and the corresponding invariant solution for some special forms of the function \(S(x,t)\) are obtained. The authors also discuss the equation (1) with function \(S(x)\) with allowed transformation and illustrate a technique for constructing wider classes of \(S(x)\) and thus new classes of solutions.
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35A22
zbMATH DE Number: 2027083
zbMATH Keywords: nonlinear Schrödinger equation
zbMATH Keywords: dimensional reduction
zbMATH Keywords: invariant solution
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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full work available at URL: s0960-0779(02)00308-9
OpenAlex ID: W1967950539
description: scientific article; zbMATH DE number 2027083