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注意:本论文已在《Physics Letters A》杂志2000年第277期212-218页发表
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范恩贵
(复旦大学 数学系,上海   200433

摘要:我们给出齐次平衡法两个新的应用,寻找非线性方程的Backlund变换和相似解,其结果与CK方法、WTC方法的结果一致。

Two new applications of the homogeneous balance method

Engui Fan )
 Physics Letters A 265 2000 353–357

Institute of Mathematics, Fudan Uniíersity, Shanghai 200433, China

Received 13 July 1999; received in revised form 3 December 1999; accepted 22 December 1999

Communicated by A.R. Bishop

Abstract:The homogeneous balance method is extended to search for Backlund transformation and similarity reduction of ¨nonlinear partial differential equations. It is shown that there exist close connections among the homogeneous balance method, WTC method and CK direct reduction method. The variant Boussinesq equations are discussed as an illustrative example. Their Backlund transformation, linearization transformation and three types of similarity reductions are obtained. ¨In the meantime, some new travelling wave solutions also are found. q2000 Published by Elsevier Science B.V. All rights reserved.
Keywords:
Homogeneous balance method; Backlund transformation; Similarity reduction; Travelling wave solution¨

 

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