此論文，我們討論黎曼空間的理論及在黎曼空間上積分的計算，接著討論橢圓函數。
最後，利用這兩個理論討論非線性薛丁格方程的特殊解。

In this paper, we study the theory of Riemann Surfaces of genus N and the numerical computation of path integrals on those Riemann Surfaces. We then study the classical theory of the elliptic functions.
Finally, we apply both theorys to solve some special solutions of Nonlinear Schrodinger Equation.

Contents
Abstract
1 Introduction
2 Riemann Surface
2.1 Construct of Riemann Surfaces of genus N
2.2 The Integrals of f(z) over a,b Cycles with Horizontal Cutstruct
2.3 The Integrals of f(z) over a,b Cycles with Vertical Cutstruct
2.4 The Integrals of f(z) over a,b Cycles with Slant Cutstruct
3 Elliptic Functions
3.1 Elliptic Functions. General theorem and The Weierstrassian Functions
3.2 The Theta Functions

3.3 The Jaobian Elliptic Functions

4 The Jaobian Elliptic Functions and The Nonlinear Schrodinger Equation
5 Conclusion
Appendix
References

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