擾動非線性薛丁格方程的計算分析

Abstract

我們考慮擾動非線性Schrodinger 方程,截取其N模常微分方程系統.在此 篇論文中,我們最主要的工作是發展一套數值計算理論與方法來探討此系 統之分歧與穩定性質.並由此預測NLS 偏微分方程的相關性質. 我們在數 學軟體Mathematica中發展出數值運算方法. 針對其它的非線性常微系統, 這套方法經過簡單之修改即可加以利用. We consider the perturbed nonlinear schrodinger equation and its N-mode truncation nonlinear ODE system. In this paper, we mainly develop the continuation and local bifurcation code to investigate the bifurcation and stability behaviors of the short time solutions of the nonlinear ODE system. From which, we are able to predict some of the corresponding NLS PDE dynamics. The code is developed in Mathematica, and is easily modified to perform in other nonlinear ODE system.