高阶广义(3 + 1)维Kadomtsov-Petviashivilli方程新的显式解

J4 ›› 2013, Vol. 30 ›› Issue (4): 391-397.

高阶广义(3 + 1)维Kadomtsov-Petviashivilli方程新的显式解

李宁刘希强

聊城大学数学科学学院，山东聊城 252059

收稿日期:2013-01-04 修回日期:2013-03-20 出版日期:2013-07-28 发布日期:2013-07-06
通讯作者: 刘希强 (1957-)，山东菏泽人，教授，博士，研究方向为非线性微分方程系统. E-mail:liuxiq@sina.com.
作者简介:李宁山东枣庄人，硕士，研究方向为非线性偏微分方程解的研究.E-mail:ln1011@163.com
基金资助:
The project is supported by National Natural Science Foundation of China and China Academy of Engineering Physics (11076015).

New explicit solutions of generalized (3 + 1)-dimensional higher-order Kadomtsov-Petviashivilli equation

LI Ning，LIU Xiqiang

School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China

Received:2013-01-04 Revised:2013-03-20 Published:2013-07-28 Online:2013-07-06

摘要/Abstract

摘要： 利用广义的代数方法,研究了高阶广义（3+1）维Kadomtsov-Petviashivilli方程，得到了许多新的显式解，这些解包括椭圆函数解，双曲函数解，三角函数解等。

关键词: 非线性方程, 显式解, 广义代数方法, 广义KP方程, 齐次平衡法

Abstract: By applying the generalized algebraic method, the generalized (3+1)-dimensional Kadomtsov-Petviashivilli equation was studied. Some new explicit solutions of the generalized (3+1)-dimensional Kadomtsov-Petviashivilli equations were obtained, which included Jacobi elliptic function solutions, hyperbolic function solutions, trigonometric function solutions and so on.

Key words: nonlinear equation, explicit solutions, generalized algebraic method, generalized Kadomtsov-Petviashivilli equation, homogeneous balance principle

中图分类号:

O175.2

李宁刘希强. 高阶广义(3 + 1)维Kadomtsov-Petviashivilli方程新的显式解[J]. J4, 2013, 30(4): 391-397.

LI Ning，LIU Xiqiang. New explicit solutions of generalized (3 + 1)-dimensional higher-order Kadomtsov-Petviashivilli equation [J]. J4, 2013, 30(4): 391-397.

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