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).
Received: 12 February 2008
Revised: 24 March 2008
Accepted manuscript online:
Fund: Project supported
by the National Natural Science Foundation of China (Grant
No 10647112) and the Foundation of Donghua University.
Cite this article:
Ma Hong-Cai (马红彩), Ge Dong-Jie (葛东杰), Yu Yao-Dong (于耀东) New periodic wave solutions, localized excitations and their interaction for 2+1-dimensional Burgers equation 2008 Chin. Phys. B 17 4344
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