中国物理B ›› 2005, Vol. 14 ›› Issue (9): 1698-1706.doi: 10.1088/1009-1963/14/9/003

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Applications of F-expansion method to the coupled KdV system

李保安1, 王明亮2   

  1. (1)College of Science, Henan University of Science and Technology,Luoyang 471003, China;Department of Mathematics, Jilin University, Changchun 130000, China; (2)College of Science, Henan University of Science and Technology,Luoyang 471003, China;Department of Mathematics, Lanzhou University, Lanzhou 730000, China
  • 收稿日期:2005-03-15 修回日期:2005-04-22 出版日期:2005-09-20 发布日期:2005-09-20
  • 基金资助:
    Project supported by the Natural Science Foundation of Henan Province of China (Grant No 0111050200) and the Science Foundation of Henan University of Science and Technology (Grant Nos 2004ZY040 and 2004ZD002).

Applications of F-expansion method to the coupled KdV system

Li Bao-An (李保安)ab, Wang Ming-Liang (王明亮)ac   

  1. a College of Science, Henan University of Science and Technology,Luoyang 471003, Chinab Department of Mathematics, Jilin University, Changchun 130000, China; c Department of Mathematics, Lanzhou University, Lanzhou 730000, China
  • Received:2005-03-15 Revised:2005-04-22 Online:2005-09-20 Published:2005-09-20
  • Supported by:
    Project supported by the Natural Science Foundation of Henan Province of China (Grant No 0111050200) and the Science Foundation of Henan University of Science and Technology (Grant Nos 2004ZY040 and 2004ZD002).

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摘要： An extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics is presented, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed more recently. By using the homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by Jacobi elliptic functions for the coupled KdV equations are derived. In the limit cases, the solitary wave solutions and the other type of travelling wave solutions for the system are also obtained.

关键词: coupled KdV equations, extended F-expansion method, Jacobi elliptic functions, periodic wave solutions, solitary wave solutions

Abstract: An extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics is presented, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed more recently. By using the homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by Jacobi elliptic functions for the coupled KdV equations are derived. In the limit cases, the solitary wave solutions and the other type of travelling wave solutions for the system are also obtained.

Key words: coupled KdV equations, extended F-expansion method, Jacobi elliptic functions, periodic wave solutions, solitary wave solutions

中图分类号:  (Partial differential equations)

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