Gardner-Kadomtsev-Petviashvili方程的精确行波解与分支

Bifurcation and Exact Travelling Wave Solutions for Gardner-Kadomtsev-Petviashvili Equation

本文讨论Gardner—Kadomtsev—Petviashvili方程的行波解，该方程在物理中有广泛应用．我们运用动力系统分支理论，首先得到了方程的分支和相图，然后通过讨论参数的范围得到了精确行波解的所有形式，其中包括孤波解，周期波解。

In this paper, we consider the exact travelling wave solutions of the Gardner- Kadomtsev-Petviashvili equation, which has widespread applications in physics. With the bifurcation theory of dynamical systems, we first get all bifurcations and phrase portraits of the equation and then by discussing the range of the parameter exact parametric representations of all wave solutions are given, including solitary wave solution, periodic wave solution, kink （antbkink） wave solution and breaking wave solution.