用(G′/G)展开法求解非线性偏微分方程精确解

Using(G′/G) Expansion Method to Find Exact Solutions of Nonlinear Partial Differential Equation

本文对(G′/G)展开法中的一类辅助方程—二阶线性常微分方程进行扩展求解,得到了此辅助方程更多形式的新精确解.借助Maple软件,利用此(G′/G)展开法求解了(3+1)-维potential-YTSF方程和(2+1)-维破裂孤子方程,得到了方程大量的新的精确解,包括含参数的双曲函数解和三角函数解.该方法直接简单并能构造出非线性偏微分方程更丰富的精确解,为求解非线性偏微分方程提供了一个更强大的方法.

In this paper,an auxiliary equation for the（G′/G） expansion method,a secondorder linear ordinary differential equation is extended to solve.We get more forms of new exact solutions for the auxiliary equation.With the help of Maple,this method is applied to construct many new exact solutions of the（3 ＋ 1）-dimensional potential-YTSF equation and the（2 ＋ 1）-dimensional breaking soliton equation including the hyperbolic function solutions and the trigonometric function solutions with parameters.It provides a simple,straight-forward and more powerful way for solving nonlinear partial differential equations.