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:我们给出一种广义Tanh函数法,可用于得到非线性方程多种行波解,有趣的是其中一个参数的符号可用于判断行波解的形状和数量。 Extended tanh-function method and its applications to nonlinear equations Engui
Fan 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.
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