- 學位論文
離散薛丁格方程的史特萊卡斯估計
Strichartz Estimate for Discrete Schrodinger Equation
並列摘要
In this paper we show the Strichartz estimate to the discrete Schr"{o}dinger equation. The continuous Strichartz is essential for the proof of the existence of solution of nonlinear Schr"{o}dinger equation in some function space[3]. It is believed that this is also a key step to the proof of the convergence for finite difference method for nonlinear Schrodinger equation.
參考文獻
ibitem{1} J. Bergh and J.Lofstrom, Interpolation Spaces: An Introduction, Springer-verlag, New York, 1976.
ibitem{2} T. Cazenave and F. B. Weissler, The Cauchy problem for the nonlinear Schrodinger Equation in $H^1$ Manuscripta Math. 61(1988), 477-494.
ibitem{3} T. Cazenave, An Introduction to nonlinear Schrodinger Equations, 3rd edition, Inst. de Matematica, UFRJ, 1996.
ibitem{4} I-Liang Cheng and Qianshun Chang, Stability and Convergence for Finite Difference Methods for Nonlinear Schrodinger Equation, 2004.
ibitem{5} J. Ginibre and G. Velo, Smoothing Properties and Retarded estimates for Some Dispersive Evolution Equations, Comm. Math. Phys. 123(1989), 535-573.
延伸閱讀
- Chen, J. H. (2010). 薛丁格方程的 Strichartz 估計與長波短波交互作用方程式的半古典極限 [master's thesis, National Chiao Tung University]. Airiti Library. https://doi.org/10.6842/NCTU.2010.00212
- 林樂（2014）。發展具頻散關係及辛結構保持之時域有限差分法求解非線性薛丁格方程〔碩士論文，國立臺灣大學〕。華藝線上圖書館。https://doi.org/10.6342/NTU.2014.02912
- Chen, D. Y. (2011). 一維度薛丁格算子其特徵值間距的探討 [doctoral dissertation, National Tsing Hua University]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0016-1908201112580817
- Lin, P. Y. (2014). 以半顯隱Runge-Kutta及擬譜法求解薛丁格方程 [master's thesis, National Chiao Tung University]. Airiti Library. https://doi.org/10.6842/NCTU.2014.00001
- Ming, W. S. (2008). Schrodinger Equation with a Complex potential [master's thesis, National Tsing Hua University]. Airiti Library. https://doi.org/10.6843/NTHU.2008.00525