(2 + 1)-维K-P方程精确解的研究

Study on Exact Solutions of (2 + 1)-Dimensional K-P Equation

摘要: 本文主要采用动力系统方法对(2 + 1)维Kadmotsev and Petviashvili (KP)方程进行研究，通过引入行波变换，将原(2 + 1)维K-P方程转化为常微分方程组。之后，对这个方程组的奇点，对应的分支和相图进行分析。最后，运用Maple软件求得用原方程的解，包括尖波解，周期波解。

Abstract: In this paper, we mainly use the dynamical systems method to solve the (2 + 1) dimensional KP equation. By introducing the traveling wave transformation, the original (2 + 1) dimensional KP equation is transformed into ordinary differential equations. After that, we analyze the singular points, the corresponding bifurcation and phase diagram of the system. Finally, the solution of the original equation is obtained by using the Maple software, including the sharp wave solutions and periodic wave solutions.