Sine-Gordon與非線性Schrodinger有限項切割常微方程之計算性分歧理論

Abstract

我們依據參考文獻[10]中的連續法及局部分岐理論,發展出自己的數值方 法,來檢試Sine-Gordon 與非線性Schrodinger之有限項切割常微分方程之 分歧性質,進以完成它們的分歧圖形.我們發現我們所得的結果與參考文獻 [9],[10]中的結果一致.除了標準的數值分析方法之外. 我們採用 Mathematica 應用軟體來分析. In this thesis, according to the theory of continuation and local bifurcation [10], we develop our own numerical code to investigate the bifurcations of finite-mode truncation nonlinear Schrodinger and Sine-Gordon ODEs. Combining the theoretic arguments and the numerical computations, we complete the bifurcation diagrams. Our results are consistent with the results done by [9], [10]. Besides the standard numerical analysis, our main computational software is Mathematica. We test the codes in the Sun-Sparc Workstation.