对Tanh函数法的推广及其在非线性方程中的应用

为了得到非线性偏微方程的行波解,提出了一种推广的tanh函数法.这种方法的主要思想是充分利用涉及两个参变量的广义Riccati方程,用它的解去代替tanh函数解,并且能从参数的符号准确地判断出行波解的类型和个数.

Extended Tanh-function Method and its Applications to Nonlinear Equations

5BAn extended tanh-function method is proposed for constructing multiple traveling wave solutions of nonlinear partial differential equations in a unified way. The key idea of this method is to take full advantage of a generalized Riccati equation involving two parameters and use its solutions to replace the tanh function in the tanh-function method. It is quite interesting that the sign of the parameters can be used to exactly judge the numbers and types of these traveling wave solutions.