中国物理B ›› 2007, Vol. 16 ›› Issue (2): 310-317.doi: 10.1088/1009-1963/16/2/007

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New travelling wave solutions for combined KdV-mKdV equation and (2+1)-dimensional Broer-Kaup-Kupershmidt system

杨先林, 唐驾时   

  1. Department of Engineering Mechanics, Hunan University, Changsha 410082, China
  • 收稿日期:2006-06-04 修回日期:2006-07-03 出版日期:2007-02-20 发布日期:2007-02-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10472029).

New travelling wave solutions for combined KdV-mKdV equation and (2+1)-dimensional Broer-Kaup-Kupershmidt system

Yang Xian-Lin(杨先林)† and Tang Jia-Shi(唐驾时)   

  1. Department of Engineering Mechanics, Hunan University, Changsha 410082, China
  • Received:2006-06-04 Revised:2006-07-03 Online:2007-02-20 Published:2007-02-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10472029).

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摘要： Some new exact solutions of an auxiliary ordinary differential equation are obtained, which were neglected by Sirendaoreji {\it et al in their auxiliary equation method. By using this method and these new solutions the combined Korteweg--de Vries (KdV) and modified KdV (mKdV) equation and (2+1)-dimensional Broer--Kaup--Kupershmidt system are investigated and abundant exact travelling wave solutions are obtained that include new solitary wave solutions and triangular periodic wave solutions.

关键词: auxiliary equation, Korteweg--de Vries (KdV)--modified KdV (mKdV) equation, Broer--Kaup--Kupershmidt system

Abstract: Some new exact solutions of an auxiliary ordinary differential equation are obtained, which were neglected by Sirendaoreji et al in their auxiliary equation method. By using this method and these new solutions the combined Korteweg--de Vries (KdV) and modified KdV (mKdV) equation and (2+1)-dimensional Broer--Kaup--Kupershmidt system are investigated and abundant exact travelling wave solutions are obtained that include new solitary wave solutions and triangular periodic wave solutions.

Key words: auxiliary equation, Korteweg--de Vries (KdV)--modified KdV (mKdV) equation, Broer--Kaup--Kupershmidt system

中图分类号:  (Ordinary differential equations)

  • 02.30.Hq
02.30.Jr (Partial differential equations) 05.45.Yv (Solitons)