中国物理B ›› 2004, Vol. 13 ›› Issue (10): 1639-1643.doi: 10.1088/1009-1963/13/10/010

• GENERAL • 上一篇    下一篇

Using symbolic computation to construct travelling wave solutions to nonlinear partial differential equations

李伟1, 谢福鼎2   

  1. (1)Department of Basic Science, Liaoning Technical University, Fuxin 123000, China; (2)MM Key Laboratory, Academy of Mathematics and System Sciences, Chinese Academy of Science, Beijing 100080, China
  • 收稿日期:2003-10-27 修回日期:2004-05-31 出版日期:2005-06-20 发布日期:2005-06-20
  • 基金资助:
    Project supported by the State Key Programme of Basic Research of China (Grant No G1998030600).

Using symbolic computation to construct travelling wave solutions to nonlinear partial differential equations

Li Wei (李伟)a, Xie Fu-Ding (谢福鼎)b   

  1. a Department of Basic Science, Liaoning Technical University, Fuxin 123000, China; b MM Key Laboratory, Academy of Mathematics and System Sciences, Chinese Academy of Science, Beijing 100080, China
  • Received:2003-10-27 Revised:2004-05-31 Online:2005-06-20 Published:2005-06-20
  • Supported by:
    Project supported by the State Key Programme of Basic Research of China (Grant No G1998030600).

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摘要： Based upon the symbolic computation and the coupled projective Riccati equation, the tanh function method is further improved. As its applications, Wu－Zhang equation (which describes a (2+1)-dimensional dispersive long wave) and the (1+1)-dimensional dispersive long wave equation obtained from Wu－Zhang equation by scaling transformation and symmetry reduction are chosen to illustrate the validity of the proposed approach.

Abstract: Based upon the symbolic computation and the coupled projective Riccati equation, the tanh function method is further improved. As its applications, Wu－Zhang equation (which describes a (2+1)-dimensional dispersive long wave) and the (1+1)-dimensional dispersive long wave equation obtained from Wu－Zhang equation by scaling transformation and symmetry reduction are chosen to illustrate the validity of the proposed approach.

Key words: Wu－Zhang equation, coupled projective Riccati equations, soliton wave solution, periodic wave solution, symbolic computation

中图分类号:  (Partial differential equations)

  • 02.30.Jr
02.60.Lj (Ordinary and partial differential equations; boundary value problems)