碩士 / 國立交通大學 / 應用數學系所 / 98 / In this paper, we study the function theory of the solutions of the nonlinear second-order equations which have the following forms,
d^2u/dt^2+PN(u)=0
where PN(u) is a polynomial of degree 2N-1 or 2N. Solutions of such equations reside on Riemann surfaces of genus N-1. We construct those Riemann surfaces with the correct algebraic structures. From which, we are able to perform path integrals on the Riemann surfaces theoretically and numerically, and, in principle, solutions can be derived. The roots of PN(u) play the essential roles in every aspects, and complex analysis is our main tool.
| Identifer | oai:union.ndltd.org:TW/098NCTU5507009 |
| Date | January 2010 |
| Creators | Wu, Yun-Ting, 吳昀庭 |
| Contributors | Lee, Jong-Eao, 李榮耀 |
| Source Sets | National Digital Library of Theses and Dissertations in Taiwan |
| Language | en_US |
| Detected Language | English |
| Type | 學位論文 ; thesis |
| Format | 178 |
Page generated in 0.0017 seconds