Extended tanh-function method and its applications to nonlinear equations
Extended tanh-function method and its applications to nonlinear equations
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DOI：
10.1016/s0375-9601(00)00725-8
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发表时间：
2000-12-04
影响因子：
2.6
通讯作者：
Fan, EG
中科院分区：
文献类型：
--
作者：
Fan, EG
提出了一种扩展 tanh 函数方法，用于统一构造非线性偏微分方程 (PDE) 的多个行波解。该方法的核心思想是充分利用带参数的Riccati方程的优点，并用其解来代替tanh函数方法中的tanh函数。有趣的是，可以通过参数的符号来准确判断这些行波解的数量和类型。此外，通过引入适当的变换，表明扩展tanh函数方法仍然适用于平衡数可以是任何非零实数的非线性偏微分方程。通过这种方法研究了一些说明性方程并找到了新的行波解。 (C) 2000 Elsevier Science B.V. 保留所有权利。
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. (C) 2000 Elsevier Science B.V. All rights reserved.