Exact solutions of KdV equation with time-dependent coefficients

被引：15

作者：

Johnpillai, A. G. ^{[2
]}

Khalique, C. M. ^{[2
]}

Biswas, Anjan ^{[1
]}

机构：

[1] Delaware State Univ, Dept Math Sci, Ctr Res & Educ Opt Sci & Applicat, Appl Math Res Ctr, Dover, DE 19901 USA

[2] North West Univ, Dept Math Sci, Int Inst Symmetry Anal & Math Modelling, ZA-2735 Mmabatho, South Africa

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2010年 / 216卷 / 10期

基金：

新加坡国家研究基金会;

关键词：

Solitons; Lie symmetries; Integrability; MKDV;

D O I：

10.1016/j.amc.2010.03.133

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the Korteweg-de Vries (KdV) equation having time dependent coefficients from the Lie symmetry point of view. We obtain Lie point symmetries admitted by the equation for various forms for the time-dependent coefficients. We use the symmetries to construct the group-invariant solutions for each of the cases of the arbitrary coefficients. Subsequently, the 1-soliton solution is obtained by the aid of solitary wave ansatz method. It is observed that the soliton solution will exist provided that these time-dependent coefficients are all Riemann integrable. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：3114 / 3119

页数：6

共 11 条

[1]

Abramowitz M., 1972, HDB MATH FUNCTIONS

[2] Solitary wave solution for the generalized KdV equation with time-dependent damping and dispersion [J].