扩展的同宿检验法与(3+1)维广义KP方程的非行波解

Extended homoclinic test approach and non-traveling wave solutions of(3+1)dimensional generalized KP equation

扩展的同宿检验法是求解非线性偏微分方程精确解非常有效的方法.该文将扩展的同宿检验法与分离变量方法相结合,探索(3+1)维广义KP方程的非行波精确解.借助数学软件工具,讨论了4种情形下的非行波精确解.进而,通过分析系数在实数域、复数域中的取值情况,得到了(3+1)维广义KP方程15种类型的精确非行波解.

The extended homoclinic test approach is an effective method to get exact solutions of nonlinear partial differential equation.In this paper,the extended homoclinic test approach and variable separation method are used to explore non-traveling wave solutions of(3+1)dimensional generalized KP equation.With the help of mathematical software,the exact non-traveling solutions in four cases are discussed.Then,by analyzing the value of coefficients in real number field and complex number field,fifteen types of exact non-traveling wave solutions of(3+1)dimensional generalized KP equation are obtained.