- 學位論文
非線性薛丁格方程的基本理論及特殊解
The Underlying Theory and Special Solutions of Nonlinear Schrödinger equation
並列摘要
In this paper, we express some special solutions q of the Nonlinear Schrodinger equation(NLS) iq_t+q_xx+2|q|^2q=0 by elliptic function dn(u,k). Since the function dn(u,k) is defined on the Riemann surface, we introduce the theory of Riemann surfaces at first, and then we introduce classical elliptic functions. Finally, we use the theory of Riemann surfaces and elliptic function to solve some special solution of NLS and analyze the degeneracies of the NLS solutions.
參考文獻
[1] Ming-Hong Fan, The Exact Theory and Numerical Computations of Pendulum Motions
on Riemann Surface of Genus N with Cut-Structure of Type C, National Chiao-Tung
University, Master thesis, 2013
[2] Jiun-Kuei Guan, Study of Underlying Theory of the Nonlinear Schrödinger Equations,
[3] 洪維恩, Mathematica 5 數學運算大師, 旗標, 2009
延伸閱讀
- Guan, J. K. (2014). 非線性薛丁格方程基本理論的探討 [master's thesis, National Chiao Tung University]. Airiti Library. https://doi.org/10.6842/NCTU.2014.00275
- Lee, C. C. (2010). 非線性薛丁格方程組的極限問題與泊松-能斯特-普朗克方程組的穩態解 [doctoral dissertation, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2010.02979
- Liu, Y. Y. (2007). 非線性薛丁格方程之基態與束縛態 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2007.01184
- Kee, L. K. (2018). 以保結構算則求解非線性薛丁格方程 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU201803907
- Zhang, Z., Wang, X., & Yao, Z. A. (2014). On the Weak Solution to a Fractional Nonlinear Schrödinger Equation. Abstract and Applied Analysis, 2014(), 941-946-895. https://doi.org/10.1155/2014/569693