Solutions, bifurcations and chaos of the nonlinear Schr?dinger equation with weak damping

doi:10.1088/1009-1963/11/3/302

中国物理B ›› 2002, Vol. 11 ›› Issue (3): 213-217.doi: 10.1088/1009-1963/11/3/302

Solutions, bifurcations and chaos of the nonlinear Schr?dinger equation with weak damping

唐驾时¹, 于德介¹, 彭解华², 颜家壬³, 海文华³

(1)Department of Mechanics, Hunan University, Changsha 410082, China; (2)Department of Mechanics, Hunan University, Changsha 410082, China; Department of Physics, Shaoyang Teacher's College, Shaoyang 422000, China; (3)Department of Physics, Hunan Normal University, Changsha 410082, China

收稿日期:2001-06-07 修回日期:2001-11-19 出版日期:2002-03-13 发布日期:2005-06-13
基金资助:
Project supported by the Natural Science Foundation of Hunan (Grant No 97JJY2075) and National Natural Science Foundation of China (Grant No 19775013).

Solutions, bifurcations and chaos of the nonlinear Schrödinger equation with weak damping

Peng Jie-Hua (彭解华)^ac, Tang Jia-Shi (唐驾时)^a, Yu De-Jie (于德介)^a,Yan Jia-Ren (颜家壬)^b, Hai Wen-Hua (海文华)^b

^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

Received:2001-06-07 Revised:2001-11-19 Online:2002-03-13 Published:2005-06-13
Supported by:
Project supported by the Natural Science Foundation of Hunan (Grant No 97JJY2075) and National Natural Science Foundation of China (Grant No 19775013).

摘要/Abstract

摘要： 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.

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.

Key words: nonlinear Schrödinger equation, nonlinear Schrödinger equation, chaos, chaos, bifurcation, bifurcation

中图分类号: (Solutions of wave equations: bound states)

03.65.Ge

05.45.Pq (Numerical simulations of chaotic systems) 05.45.Yv (Solitons)

彭解华, 唐驾时, 于德介, 颜家壬, 海文华. Solutions, bifurcations and chaos of the nonlinear Schr?dinger equation with weak damping[J]. 中国物理B, 2002, 11(3): 213-217.

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[J]. Chinese Physics, 2002, 11(3): 213-217.

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Solutions, bifurcations and chaos of the nonlinear Schr?dinger equation with weak damping

Solutions, bifurcations and chaos of the nonlinear Schrödinger equation with weak damping

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