Redundant exact solutions of nonlinear differential equations

被引：8

作者：

Kudryashov, Nikolay A. ^{[1
]}

机构：

[1] Natl Res Nucl Univ MEPHI, Dept Appl Math, Moscow 115409, Russia

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2011年 / 16卷 / 09期

关键词：

Nonlinear evolution equations; Nonlinear ordinary differential equation; Exact solutions; Redundant exact solution; TRAVELING-WAVE SOLUTIONS; TANH-FUNCTION METHOD; KDV;

D O I：

10.1016/j.cnsns.2010.12.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We analyze the paper by Wazwaz and Mehanna [Wazwaz AM, Mehanna MS. A variety of exact travelling wave solutions for the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation. Appl Math Comput 2010;217:1484-90]. The authors claim that they have found exact solutions of the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation using the tanh-coth method and the Exp-function method. We demonstrate that two of their solutions are incorrect. All the others can be simplified and they are the partial cases of the well-known solution. Wazwaz and Mehanna made a number of typical mistakes in finding exact solutions of nonlinear differential equations. Taking the results of this paper we introduce the definition of redundant exact solutions for the nonlinear ordinary differential equations. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：3451 / 3456

页数：6

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