黎曼空間和橢圓函數的理論及其在非線性薛丁格方程上的應用

Abstract

此篇論文中，我們學習非線性薛丁格方程的解的函數理論，這些解有開根號的形式。此方程的解存在於N-1相黎曼空間上，所以我們先探討黎曼空間的理論，接著我們學習橢圓函數來解特殊的非線性薛丁格方程的解，並且討論解的相關的性質。

In this paper, we study the function theory of the solutions of the nonlinear Schrodinger equation (NLS), and these solutions have the radical forms. Solutions of such equation resides on the the Riemann surface of genus N-1 so we first study the theory of Riemann surface. Then we study the classical elliptic functions to solve some special solutions of NLS and analyze the associated properties.