黎曼空間與橢圓函數的理論與Korteweg-deVries方程的應用

Abstract

Korteweg-deVries方程是個非線性微分方程[參考文獻 [5][6][7]]，我們研究這方程有兩個方面。首先，我們研究了黎曼空間的函數空間的解和非線性逼近。 再者，我們研究古典橢圓函數並利用Weierstrassian橢圓函數來分析KdV方程來尋找特殊解和相關性質。

The Korteweg-deVries equation is a nonlinear equation[Reference [5][6][7]], we study it in two aspects. First, we study the function spaces of its solutions and nonlinear approximations, which are Riemann surfaces. Secondly, we study theory of the classical elliptic function and use Weierstrassian function to analyze KdV equation to find some special solution and related properties.