利用函数变换构造非线性发展方程新的复合型精确解

Constructing New Exact Complex Solutions to Nonlinear Evolution Equations with the Function Transformation

为了获得非线性发展方程新的复合型精确解,本文引入了一种函数变换,把常系数的非线性发展方程转化为二阶非齐次线性常微分方程。在此基础上利用常微分方程的理论和符号计算系统Mathematica及用(2+1)维修改的色散水波方程,构造了新的复合型精确解。这些解中包括指数函数、三角函数和有理函数,通过这几种形式组合而成的复合型单孤子解和双孤子解。

In this paper,nonlinear evolution equations with constant coefficients are changed into the second order non-homogenous ordinary differential equations through introducing a function transformation to search for complex exact solutions of some nonlinear evolution equations.Based on the theory of ordinary differential equations,the（2 ＋ l）-dimensional modified dispersion wave equation is chosen as an example and the new complex exact solutions are obtained with the help of symbolic computation system Mathematica,which include single solitary solutions and double solitary solutions of the composite type composed by exponential function,triangular function and rational function in different forms.