N-階非線性常微方程式分歧現象分析

Abstract

我們發展一套理論及數值的工具以探索高維非線性常微方程的分歧動態現 象.在稍後內容中,並將以此測試 N-mode 薛丁格方程式,展現與參考文獻 [11]完全一致的結果. In this thesis, we develped both the theoretic and numerical tools to investigate the bifurcation dynamics of the general nonlinear,high-dimensional ODEs. Our numerical code is then developed and applied to the N-mode truncated, perturbed nonlinear Schrodinger equation (which is specified later) to do the pratical computations. The results are completely consistent with the previous work done by Chuyu Xiong [11], which is also the main reference in our study.