Variable Separation Approach to Solve (2+1)-Dimensional Generalized Burgers System: Solitary Wave and Jacobi Periodic Wave Excitations**The project supported by National Natural Science Foundation of China under Grant No. 10172056, the Natural Science Foundation of Zhengjiang Province, and the Foundation of Zhengjiang Lishui College under Grant Nos. KZ03009 and KZ03005

Abstract

By means of the standard truncated Painlevé expansion and a variable separation approach, a general variable separation solution of the generalized Burgers system is derived. In addition to the usual localized coherent soliton excitations like dromions, lumps, rings, breathers, instantons, oscillating soliton excitations, peakons, foldons, and previously revealed chaotic and fractal localized solutions, some new types of excitations — compacton and Jacobi periodic wave solutions are obtained by introducing appropriate lower dimensional piecewise smooth functions and Jacobi elliptic functions.