a Department of Mechanics, Hunan University, Changsha 410082, China; b Department of Physics, Hunan Normal University, Changsha 410082, China; c Department of Physics, Shaoyang Teacher's College, Shaoyang 422000, China
Abstract Using the wave packet theory, we obtain all the solutions of the weakly damped nonlinear Schr?dinger equation. These solutions are the static solution, and solutions of planar wave, solitary wave, shock wave and elliptic function wave and chaos. The bifurcation phenomenon exists in both steady and non-steady solutions. The chaotic and periodic motions can coexist in a certain parametric space region.
Received: 07 June 2001
Revised: 19 November 2001
Accepted manuscript online:
Fund: Project supported by the Natural Science Foundation of Hunan (Grant No 97JJY2075) and National Natural Science Foundation of China (Grant No 19775013).
Cite this article:
Peng Jie-Hua (彭解华), Tang Jia-Shi (唐驾时), Yu De-Jie (于德介), Yan Jia-Ren (颜家壬), Hai Wen-Hua (海文华) Solutions, bifurcations and chaos of the nonlinear Schrödinger equation with weak damping 2002 Chinese Physics 11 213
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