中国物理B ›› 2001, Vol. 10 ›› Issue (8): 694-697.doi: 10.1088/1009-1963/10/8/304

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NEW EXPLICIT AND EXACT TRAVELLING WAVE SOLUTIONS FOR A COMPOUND KdV－BURGERS EQUATION

张鸿庆1, 闫振亚1, 夏铁成2   

  1. (1)Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China; (2)Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China; Department of Mathematics, Jinzhou Normal University Jinzhou 121000, China
  • 收稿日期:2000-05-17 修回日期:2001-01-22 出版日期:2001-08-15 发布日期:2005-06-12
  • 基金资助:
    Project supported by the National Key Basic Research Development project of China (Grant No. 1998030600), the National Natural Science Foundation of China (Grant No. 10072013) and Educational Committee of Liaoning Province (Grant No. 990421093).

NEW EXPLICIT AND EXACT TRAVELLING WAVE SOLUTIONS FOR A COMPOUND KdV－BURGERS EQUATION

Xia Tie-cheng (夏铁成)ab, Zhang Hong-qing (张鸿庆)a, Yan Zhen-ya (闫振亚)a    

  1. a Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China; b Department of Mathematics, Jinzhou Normal University Jinzhou 121000, China
  • Received:2000-05-17 Revised:2001-01-22 Online:2001-08-15 Published:2005-06-12
  • Supported by:
    Project supported by the National Key Basic Research Development project of China (Grant No. 1998030600), the National Natural Science Foundation of China (Grant No. 10072013) and Educational Committee of Liaoning Province (Grant No. 990421093).

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摘要： In this paper, new explicit and exact travelling wave solutions for a compound KdV－Burgers equation are obtained by using the hyperbola function method and the Wu elimination method, which include new solitary wave solutions and periodic solutions. Particularly important cases of the equation, such as the compound KdV, mKdV－Burgers and mKdV equations can be solved by this method. The method can also solve other nonlinear partial differential equations.

Abstract: In this paper, new explicit and exact travelling wave solutions for a compound KdV－Burgers equation are obtained by using the hyperbola function method and the Wu elimination method, which include new solitary wave solutions and periodic solutions. Particularly important cases of the equation, such as the compound KdV, mKdV－Burgers and mKdV equations can be solved by this method. The method can also solve other nonlinear partial differential equations.

Key words: compound KdV－Burgers equation, travelling wave solution, Wu elimination method

中图分类号:  (Solitons)

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