- 學位論文
黎曼空間與橢圓函數的理論與Korteweg-deVries方程的應用
The Theory of Riemann Surface and Elliptic Function with Application to the Korteweg-deVries equation
摘要
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。
關鍵字
黎曼空間並列摘要
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.
並列關鍵字
Riemann Surface參考文獻
[1]Geore Springer, Introduction to Riemann Surfaces, Chelsea, 1981.
[2]James Ward Brown and Ruel V. Churchill, Complex Variables and Applications 7th ed, McGraw-Hill, 2003.
[5]Thomas Kappeler, KdV & KAM, Springer, 2003.
[7]Chun-Ying Juan, Darboux transformation of the KdV equation, NCTU, Master thesis, 2006.
[10]Wei-Long Tu, Theory and Applications of Riemann Surfaces of genus N, NCTU, Master thesis, 2010.
延伸閱讀
- Tzeng, T. S. (2012). 正弦戈方程在黎曼空間與橢圓函數上理論及應用 [master's thesis, National Tsing Hua University]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0016-2511201310530341
- 顏致遠（2013）。半古典橢圓波茲曼模型方程式的直接解法〔碩士論文，國立臺灣大學〕。華藝線上圖書館。https://doi.org/10.6342/NTU.2013.01901
- Lin, T. H. (2009). 計算二元體上橢圓曲線群之群秩：SEA演算法的實作 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2009.02400
- Roy, R. (1984). THE SERRE DUALITY THEOREM FOR RIEMANN SURFACES. International Journal of Mathematics and Mathematical Sciences, 1984(), 397-402. https://doi.org/10.1155/S0161171284000405
- Zhang, T., & Shen, C. (2014). Regularization of the Shock Wave Solution to the Riemann Problem for the Relativistic Burgers Equation. Abstract and Applied Analysis, 2014(), 408-417-145. https://doi.org/10.1155/2014/178672