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山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (2): 77-84.doi: 10.6040/j.issn.1671-9352.0.2016.182

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扩展的KP-Benjamin-Bona-Mahoney方程的对称、约化和精确解

李玉,刘希强*   

  1. 聊城大学数学科学学院, 山东 聊城 252059
  • 收稿日期:2016-04-26 出版日期:2017-02-20 发布日期:2017-01-18
  • 通讯作者: 刘希强(1957— ),男,博士,教授,研究方向为非线性发展方程系统. E-mail:liuxiq@sina.com E-mail:liyu910118@sina.com
  • 作者简介:李玉(1991— ),女,硕士研究生,研究方向为非线性发展方程求解研究. E-mail:liyu910118@sina.com
  • 基金资助:
    国家自然科学基金与中国工程物理研究院基金课题(NSAF:11076015)

Symmetry, reduction and exact solutions of the extended KP-Benjamin-Bona-Mahoney equation

LI Yu, LIU Xi-qiang*   

  1. School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, Shandong, China
  • Received:2016-04-26 Online:2017-02-20 Published:2017-01-18

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摘要： 应用经典李群方法得到了扩展的KP-Benjamin-Bona-Mahoney方程的对称和约化方程。通过求解得到的约化方程,结合(G'/G)-展开法和tanh函数展开法以及Riccati辅助方程,求出了该方程的一些精确解,包括行波解、有理函数解、双曲函数解、三角函数解等。最后,利用对称和伴随方程,求出了该方程的守恒律。

关键词: KP-Benjamin-Bona-Mahoney方程, 李点对称, 守恒律, 精确解, 约化方程

Abstract: By applying the direct symmetry method, the classical Lie symmetry and reduced equation of the extended KP-Benjamin-Bona-Mahoney equation are obtained. At the same time, through the reduced equation, a great many of solutions are derived by solving the reduction equations with(G'/G)-expansion method and the tanh function expansion method and Riccati auxiliary equation, including travelling wave solutions, the rational function solutions, hyperbolic function solutions, the trigonometric function solutions and so on. Finally, the conservation laws of the equation are obtained by using the symmetry and adjoint equations.

Key words: KP-Benjamin-Bona-Mahoney equation, reduction equation, conservation laws, exact solution, Lie point symmetry

中图分类号: 

  • O175.2
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