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ע⣺ՓڡPhysics Letters A2000277212-218l
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Two new applications of the homogeneous balance method

Engui Fan )
 Physics Letters A 265 2000 353C357

Institute of Mathematics, Fudan Uniersity, 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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