注意:本论文已在《Physics
Letters A》杂志2000年第277期212-218页发表 范恩贵 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 ) 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.
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