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Chin. Phys., 2007, Vol. 16(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

Wu Xiao-Feia, Zhu Jia-Minb, Ma Zheng-Yib
a College of Information, Zhejiang Lishui University, Lishui 323000, China; b College of Information, Zhejiang Lishui University, Lishui 323000, China;Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
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.
Keywords:  extended Jacobian elliptic function expansion approach      discrete doubly periodic solutions      discrete solitary wave solutions      semi-discrete coupled mKdV equations  
Received:  13 November 2006      Revised:  06 January 2007      Published:  20 August 2007
PACS:  05.45.Yv (Solitons)  
  02.30.Jr (Partial differential equations)  
  02.30.Mv (Approximations and expansions)  
Fund: 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).

Cite this article: 

Wu Xiao-Fei, Zhu Jia-Min, Ma Zheng-Yi Discrete doubly periodic and solitary wave solutions for the semi-discrete coupled mKdV equations 2007 Chin. Phys. 16 2159

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