A numerical method for finding soliton solutions in nonlinear differential equations

被引：2

作者：

Savenkova N.P. ^{[1
]}

Laponin V.S. ^{[1
]}

机构：

[1] Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow

来源：

Moscow University Computational Mathematics and Cybernetics | 2013年 / 37卷 / 2期

关键词：

convergence; iterative method; nonlinearity; Soliton solution;

D O I：

10.3103/S0278641913020076

中图分类号：

学科分类号：

摘要：

An iterative method for finding soliton solutions to Korteweg-de Vries and sine-Gordon equations, and for nonlinear Schrodinger equations with cubic nonlinearity, is proposed. In addition, the existence of soliton solutions depending on control parameters is investigated for femtosecond pulse propagation problems in media with cubic nonlinearity. In contrast to other approaches to finding soliton solutions, the proposed method has a high convergence rate, can be applied to multidimensional problems, and does not require special selection of the initial approximation. © 2013 Allerton Press, Inc.

引用

页码：49 / 54

页数：5

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