臺灣博碩士論文加值系統

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.