中国物理B ›› 2008, Vol. 17 ›› Issue (12): 4344-4353.doi: 10.1088/1674-1056/17/12/002

• GENERAL • 上一篇    下一篇

New periodic wave solutions, localized excitations and their interaction for 2+1-dimensional Burgers equation

马红彩, 葛东杰, 于耀东   

  1. Department of Applied Mathematics, College of Science, Donghua University, Shanghai 201620, China
  • 收稿日期:2008-02-12 修回日期:2008-03-24 出版日期:2008-12-20 发布日期:2008-12-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10647112) and the Foundation of Donghua University.

New periodic wave solutions, localized excitations and their interaction for 2+1-dimensional Burgers equation

Ma Hong-Cai (马红彩), Ge Dong-Jie (葛东杰), Yu Yao-Dong (于耀东)   

  1. Department of Applied Mathematics, College of Science, Donghua University, Shanghai 201620, China
  • Received:2008-02-12 Revised:2008-03-24 Online:2008-12-20 Published:2008-12-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10647112) and the Foundation of Donghua University.

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摘要： Based on the B?cklund method and the multilinear variable separation approach (MLVSA), this paper finds a general solution including two arbitrary functions for the (2+1)-dimensional Burgers equations. Then a class of new doubly periodic wave solutions for (2+1)-dimensional Burgers equations is obtained by introducing appropriate Jacobi elliptic functions, Weierstrass elliptic functions and their combination in the general solutions (which contains two arbitrary functions). Two types of limit cases are considered. Firstly, taking one of the moduli to be unity and the other zero, it obtains particular wave (called semi-localized) patterns, which is periodic in one direction, but localized in the other direction. Secondly, if both moduli are tending to 1 as a limit, it derives some novel localized excitations (two-dromion solution).

Abstract: Based on the B?cklund method and the multilinear variable separation approach (MLVSA), this paper finds a general solution including two arbitrary functions for the (2+1)-dimensional Burgers equations. Then a class of new doubly periodic wave solutions for (2+1)-dimensional Burgers equations is obtained by introducing appropriate Jacobi elliptic functions, Weierstrass elliptic functions and their combination in the general solutions (which contains two arbitrary functions). Two types of limit cases are considered. Firstly, taking one of the moduli to be unity and the other zero, it obtains particular wave (called semi-localized) patterns, which is periodic in one direction, but localized in the other direction. Secondly, if both moduli are tending to 1 as a limit, it derives some novel localized excitations (two-dromion solution).

Key words: (2+1)-dimensional Burgers equation, mutilinear variable separation approach, periodic wave solutions, localized excitation

中图分类号:  (Solitons)

  • 05.45.Yv
02.30.Jr (Partial differential equations)