闵迪. 非线性发展方程的求解与达布变换[D]: [硕士学位论文]. 大连: 辽宁师范大学, 2010.
被以下文章引用:
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标题:
(2 + 1)-维K-P方程精确解的研究Study on Exact Solutions of (2 + 1)-Dimensional K-P Equation
作者:
卫慧芳
关键字:
动力系统, 孤立波解, K-P方程Dynamical Systems, Sharp Wave Solution, K-P Equation
期刊名称:
《Advances in Applied Mathematics》, Vol.5 No.3, 2016-08-30
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。
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.