中国物理B ›› 2003, Vol. 12 ›› Issue (2): 131-135.doi: 10.1088/1009-1963/12/2/301

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New periodic solutions to a generalized Hirota－Satsuma coupled KdV system

魏小鹏1, 闫庆友2, 张玉峰3   

  1. (1)Center of Advanced Design Technology, Dalian University, Dalian 116622, China; (2)Center of Advanced Design Technology, Dalian University, Dalian 116622, China; School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China; (3)Institute of Computation Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China; School of Information Science and Engineering, Shandong University of Science and Technology, Taian 271019, China
  • 收稿日期:2002-07-27 修回日期:2002-09-04 出版日期:2003-02-16 发布日期:2005-03-16
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 50275013 and G60174037).

New periodic solutions to a generalized Hirota－Satsuma coupled KdV system

Yan Qing-You (闫庆友)ab, Zhang Yu-Feng (张玉峰)cd, Wei Xiao-Peng (魏小鹏)a   

  1. a Center of Advanced Design Technology, Dalian University, Dalian 116622, China; b School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China; c Institute of Computation Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, Chinad School of Information Science and Engineering, Shandong University of Science and Technology, Taian 271019, China
  • Received:2002-07-27 Revised:2002-09-04 Online:2003-02-16 Published:2005-03-16
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 50275013 and G60174037).

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摘要： Using expansions in terms of the Jacobi elliptic cosine function and third Jacobi elliptic function, some new periodic solutions to the generalized Hirota－Satsuma coupled KdV system are obtained with the help of the algorithm Mathematica. These periodic solutions are also reduced to the bell-shaped solitary wave solutions and kink-shape solitary solutions. As special cases, we obtain new periodic solution, bell-shaped and kink-shaped solitary solutions to the well-known Hirota－Satsuma equations.

Abstract: Using expansions in terms of the Jacobi elliptic cosine function and third Jacobi elliptic function, some new periodic solutions to the generalized Hirota－Satsuma coupled KdV system are obtained with the help of the algorithm Mathematica. These periodic solutions are also reduced to the bell-shaped solitary wave solutions and kink-shape solitary solutions. As special cases, we obtain new periodic solution, bell-shaped and kink-shaped solitary solutions to the well-known Hirota－Satsuma equations.

Key words: periodic solution, Hirota－Satsuma coupled KdV system, Jacobi elliptic function

中图分类号:  (Function theory, analysis)

  • 02.30.-f