中国物理B ›› 2007, Vol. 16 ›› Issue (8): 2159-2166.doi: 10.1088/1009-1963/16/8/003

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Discrete doubly periodic and solitary wave solutions for the semi-discrete coupled mKdV equations

吴晓飞1, 朱加民2, 马正义2   

  1. (1)College of Information, Zhejiang Lishui University, Lishui 323000, China; (2)College of Information, Zhejiang Lishui University, Lishui 323000, China;Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • 收稿日期:2006-11-13 修回日期:2007-01-06 出版日期:2007-08-20 发布日期:2007-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10272071) and the Natural Science Foundation of Zhejiang Lishui University of China (Grant Nos KZ05004 and KY06024).

Discrete doubly periodic and solitary wave solutions for the semi-discrete coupled mKdV equations

Wu Xiao-Fei(吴晓飞)a)†, Zhu Jia-Min(朱加民)a)b), and Ma Zheng-Yi(马正义)a)b)   

  1. a College of Information, Zhejiang Lishui University, Lishui 323000, China; b Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • Received:2006-11-13 Revised:2007-01-06 Online:2007-08-20 Published:2007-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10272071) and the Natural Science Foundation of Zhejiang Lishui University of China (Grant Nos KZ05004 and KY06024).

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摘要： In this paper, the improved Jacobian elliptic function expansion approach is extended and applied to constructing discrete solutions of the semi-discrete coupled modified Korteweg de Vries (mKdV) equations with the aid of the symbolic computation system Maple. Some new discrete Jacobian doubly periodic solutions are obtained. When the modulus $m \rightarrow 1$, these doubly periodic solutions degenerate into the corresponding solitary wave solutions, including kink-type, bell-type and other types of excitations.

关键词: semi-discrete coupled mKdV equations, extended Jacobian elliptic function expansion approach, discrete doubly periodic solutions, discrete solitary wave solutions

Abstract: In this paper, the improved Jacobian elliptic function expansion approach is extended and applied to constructing discrete solutions of the semi-discrete coupled modified Korteweg de Vries (mKdV) equations with the aid of the symbolic computation system Maple. Some new discrete Jacobian doubly periodic solutions are obtained. When the modulus $m \rightarrow 1$, these doubly periodic solutions degenerate into the corresponding solitary wave solutions, including kink-type, bell-type and other types of excitations.

Key words: semi-discrete coupled mKdV equations, extended Jacobian elliptic function expansion approach, discrete doubly periodic solutions, discrete solitary wave solutions

中图分类号:  (Solitons)

  • 05.45.Yv
02.30.Jr (Partial differential equations) 02.30.Mv (Approximations and expansions)