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注意:本論文已在《Physics Letters A》雜志2000年第277期212-218頁發表
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范恩貴
(復旦大學 數學系,上海   200433

 摘要:我們給出一種廣義Tanh函數法,可用于得到非線性方程多種行波解,有趣的是其中一個參數的符號可用于判斷行波解的形狀和數量。
關鍵詞

Extended tanh-function method and its applications to nonlinear equations

Engui Fan
Physics Letters A 277 (2000) 212–218

Institute of Mathematics, Fudan University, Shanghai 200433, PR China

Received 26 July 2000; received in revised form 25 October 2000; accepted 25 October 2000

Communicated by C.R. Doering

Abstract:An extended tanh-function method is proposed for constructing multiple travelling wave solutions of nonlinear partial differential equations (PDEs) in a unified way. The key idea of this method is to take full advantages of a Riccati equation involving a parameter and use its solutions to replace the tanh function in the tanh-function method. It is quite interesting that the sign of the parameter can be used to exactly judge the numbers and types of these travelling wave solutions. In addition, by introducing appropriate transformations, it is shown that the extended tanh-function method still is applicable to nonlinear PDEs whose balancing numbers may be any nonzero real numbers. Some illustrative equations are investigated by this means and new travelling wave solutions are found. 
Keywords:
Nonlinear partial differential equation; Travelling wave solution; Riccati equation; Symbolic computation

 

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