Study of the Underlying Theory of the Nonlinear Schrodinger Equations

• Main Authors: Guan, Jiun-Kuei, 管俊奎
• Other Authors: Lee, Jong-Eao
• Format: Others
• Language: en_US
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/53615207535385572019

碩士 === 國立交通大學 === 應用數學系數學建模與科學計算碩士班 === 102 === In this paper, we want to use the elliptic function dn(u; k) to express analytically some special solutions of the Nonlinear Schrὂdinger equation (NLS), iq_t+q_xx+2〖|q|〗^2 q=0 The function dn(u; k) is defined on some Riemann surface, so we first introduce the theory of Riemann surfaces, and then we introduce elliptic functions. Finally, we use theory of Riemann surfaces and elliptic functions to analyze and solve some special solutions of the NLS and discuss the degenerates of those solutions.