中国物理B ›› 2003, Vol. 12 ›› Issue (1): 1-10.doi: 10.1088/1009-1963/12/1/301

• GENERAL •    下一篇

New explicit exact solutions for a generalized Hirota-Satsuma coupled KdV system and a coupled MKdV equation

陈　勇, 闫振亚, 李　彪, 张鸿庆   

  1. Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China
  • 收稿日期:2002-01-03 修回日期:2002-09-20 出版日期:2003-01-20 发布日期:2003-01-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 1007201), the State Key Development Programme for Basic Research of China (Grant No G1998030600), and the Doctorate Fund of the State Education Commission of China (Grant No 98014119).

New explicit exact solutions for a generalized Hirota-Satsuma coupled KdV system and a coupled MKdV equation

Cheng Yong (陈　勇), Yan Zhen-Ya (闫振亚), Li Biao (李　彪), Zhang Hong-Qing (张鸿庆)   

  1. Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China
  • Received:2002-01-03 Revised:2002-09-20 Online:2003-01-20 Published:2003-01-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 1007201), the State Key Development Programme for Basic Research of China (Grant No G1998030600), and the Doctorate Fund of the State Education Commission of China (Grant No 98014119).

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摘要： In this paper, we make use of a new generalized ansatz in the homogeneous balance method, the well-known Riccati equation and the symbolic computation to study a generalized Hirota--Satsuma coupled KdV system and a coupled MKdV equation, respectively. As a result, numerous explicit exact solutions, comprising new solitary wave solutions, periodic wave solutions and the combined formal solitary wave solutions and periodic wave solutions, are obtained.

Abstract: In this paper, we make use of a new generalized ansatz in the homogeneous balance method, the well-known Riccati equation and the symbolic computation to study a generalized Hirota--Satsuma coupled KdV system and a coupled MKdV equation, respectively. As a result, numerous explicit exact solutions, comprising new solitary wave solutions, periodic wave solutions and the combined formal solitary wave solutions and periodic wave solutions, are obtained.

Key words: coupled MKdV system, Riccati equation, solitary wave solution, periodic wave solution

中图分类号:  (Partial differential equations)

  • 02.30.Jr