CHINESE JOURNAL OF PHYSICS VOL. 40, NO. 3 JUNE 2002

Singularity Structure Analysis and Abundant New Dromion-like Structures for
the (2+1)-Dimensional Generalized Burgers Equation

Yan Zhenya^*

Department of Applied Mathematics, Dalian University of Technology,

Dalian 116024, China
(Received November 23, 2001)

The Painleve (P) singularity analysis method (the WTC method, due to Weiss, Tabor and Carnevale) is a powerful tool for proving the P-property of nonlinear partial differential equations and their Bäcklund transformations. In this paper, the singularity structure analysis is performed for the (2+1)-dimensional generalized Burgers equation, $u_t+u_{xy}+uu_y+u_x\partial^{-1}_xu_y=0$, by using the WTC method; it is shown that the equation passes the Panilevé test. Based on the P-analysis, a Bäcklund transformation is obtained, and then it is used to find many exact solutions including N-soliton-like solutions and new exact solutions. Some of these obtained solutions are used to prove that the variable u_y(x,y,t), rather than the physical field u(x,y,t) in the (2+1)-dimensional generalized Burgers equation, admits abundant dromion-like solutions (exponentially localized solutions) such as point dromions, ring dromions, extended dromions, sharp dromions and oscillatory dromion solutions.

PACS. 03.40.Kf - Waves and wave propagation: general mathematical aspects.

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