中国物理B ›› 2004, Vol. 13 ›› Issue (3): 302-306.doi: 10.1088/1009-1963/13/3/007

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Travelling wave solutions for generalized symmetric regularized long-wave equations with high-order nonlinear terms

李彪1, 陈勇2   

  1. (1)Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China; Key Laboratory of Mathematics Mechanization, Chinese Academy of Sciences, Beijing 100080, China; (2)Department of Physics, Shanghai Jiaotong University, Shanghai 200030, China; Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China; Key Laboratory of Mathematics Mechanization, Chinese Academy of Sciences, Beijing 100080
  • 收稿日期:2003-05-30 修回日期:2003-09-01 出版日期:2004-03-06 发布日期:2005-07-06
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10072013), the State Key Development Program for Basic Research of China (Grant No G1998030600).

Travelling wave solutions for generalized symmetric regularized long-wave equations with high-order nonlinear terms

Chen Yong (陈勇)abc, Li Biao (李彪)bc    

  1. a Department of Physics, Shanghai Jiaotong University, Shanghai 200030, China; ; b Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China; c Key Laboratory of Mathematics Mechanization, Chinese Academy of Sciences, Beijing 100080, China
  • Received:2003-05-30 Revised:2003-09-01 Online:2004-03-06 Published:2005-07-06
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10072013), the State Key Development Program for Basic Research of China (Grant No G1998030600).

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摘要： Applying the general projective Riccati equations method, we consider the exact travelling wave solutions for generalized symmetric regularized long-wave equations with high-order nonlinear terms using symbolic computation. From our results, we not only can successfully recover some previously known travelling wave solutions found by using various tanh methods, but also can obtain some new formal solutions. The solutions obtained include kink-shaped solitons, bell-shaped solitons, singular solitons and periodic solutions.

关键词: symbolic computation, projective Riccati equations method, generalized symmetric regularized long-wave equation, soliton

Abstract: Applying the general projective Riccati equations method, we consider the exact travelling wave solutions for generalized symmetric regularized long-wave equations with high-order nonlinear terms using symbolic computation. From our results, we not only can successfully recover some previously known travelling wave solutions found by using various tanh methods, but also can obtain some new formal solutions. The solutions obtained include kink-shaped solitons, bell-shaped solitons, singular solitons and periodic solutions.

Key words: symbolic computation, projective Riccati equations method, generalized symmetric regularized long-wave equation, soliton

中图分类号:  (Solutions of wave equations: bound states)

  • 03.65.Ge
05.45.Yv (Solitons)