中山大学学报自然科学版 ›› 2010, Vol. 49 ›› Issue (3): 5-7.

• 研究论文 • 上一篇    下一篇

离散时滞KdV类方程的群不变解

赵志红1, 徐远通2, 葛渭高1   

  1. (1北京理工大学理学院, 北京 100081;2中山大学数学与计算科学学院,广东 广州 510275)
  • 收稿日期:2009-05-15 修回日期:1900-01-01 出版日期:2010-05-25 发布日期:2010-05-25

The Group Invariant Solutions of KdV Type Equation with Discrete Delay

ZHAO Zhihong 1, XU Yuantong2, GE Weigao1   

  1. (1Department of Mathematics, Beijing Institute of Technology, Beijing 100081,China;2Department of Mathematics, Sun Yatsen University, Guangzhou 510275,China)
  • Received:2009-05-15 Revised:1900-01-01 Online:2010-05-25 Published:2010-05-25

摘要: 研究时滞KdV类方程ut(t,x)+u(t,x)ux(t,x)+uxxx(t,x)=g(x,u,u(t-τ,x))的群不变解。主要方法是根据时滞微分方程等价Lie群的定义,可构造时滞KdV类方程相应的决定方程和容许Lie群,从而得到时滞KdV类方程的群不变解。

关键词: 时滞KdV类方程, 容许Lie群, 群不变解

Abstract: The group invariant solutions of the KdV type equation with discrete delay ut(t,x)+u(t,x)ux(t,x)+uxxx(t,x)=g(x,u,u(t-τ,x)) are studied. According to the definition of an equivalence Lie group for delay differential equations, we construct the determining equations and admitted Lie groups of delay KdV type equation. Then the group invariant solutions of the delay KdV type equation are obtained.

Key words: KdV type equation with discrete delay, admitted Lie group, group invariant solution

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