Sine-Gordon與非線性Schrodinger微分方程的計算性分岐理論

Abstract

我們發展一套數值的法規以探索有限切割sine-Gordon及非線性 chrodinger常微分方程式的分岐現象.藉由連續及局部分岐理論,我們將此 兩種動態系統做數值分析與計算而完成分岐圖形.而我們的結果將展現與 參考文獻[8],[11]一致的結果. In this thesis, we develop the numerical code to investigate the bifurcation behaviors of finite-mode truncated sine- Gordonnd nonlinear Schrodinger ODEs. Follow the theory of Continuationnd Local Bifurcation [8], we do numerical analysis and computations to complete the bifurcation diagrams for bothynamical systems. Both diagrams contains bifurcation points suchs turning points, pitchfork points, and Hopf bifurcation points.ur results are consistent with the results done by [8], [11]. Wevelop our codes in the software Mathematica in the Sun Sparckstations.