Abstract The dynamic properties of a cubic nonlinear Schr?dinger equation are investigated numerically by using the symplectic method with different space approximations. The behaviours of the cubic nonlinear Schr?dinger equation are discussed with different cubic nonlinear parameters in the harmonically modulated initial condition. We show that the conserved quantities will be preserved for long-time computation but the system will exhibit different dynamic behaviours in space difference approximation for the strong cubic nonlinearity.
Received: 21 April 2004
Revised: 04 November 2004
Accepted manuscript online:
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos 10171039 and 10074019), the Special Foundation for State Major Basic Research Programme of China (Grant No G1999032804) and the Young Teacher Foundation of Jilin University.
Cite this article:
Liu Xue-Shen (刘学深), Wei Jia-Yu (魏佳羽), Ding Pei-Zhu (丁培柱) Dynamic properties of the cubic nonlinear Schrödinger equation by symplectic method 2005 Chinese Physics 14 231
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