博士 / 國立交通大學 / 應用數學系所 / 98 / This dissertation investigates the dispersive limits of the nonlinear Klein-Gordon equations. First, we perform the mathematical derivation of the compressible and incompressible Euler equations from the modulated nonlinear Klein-Gordon equation. Before the formation of singularities in the limit system, the nonrelativistic-semiclassical limit is shown to be the compressible Euler equations. If we further rescale the time variable, then in the semiclassical limit (the light speed kept fixed), the incompressible Euler equations are recovered.
We also establish the singular limits including semiclassical, nonrelativistic and nonrelativistic-semiclassical limits of the Cauchy problem for the modulated defocusing nonlinear Klein-Gordon equation. For the semiclassical limit, we show that the limit wave function of the modulated defocusing cubic nonlinear Klein-Gordon equation solves the relativistic wave map and the associated phase function satisfies a linear relativistic wave equation. The nonrelativistic limit of the modulated defocusing nonlinear Klein-Gordon equation is the defocusing nonlinear Schrodinger equation. The nonrelativistic-semiclassical limit of the modulated defocusing cubic nonlinear Klein-Gordon equation is the classical wave map for the limit wave function and typical linear wave equation for the associated phase function.
| Identifer | oai:union.ndltd.org:TW/098NCTU5507010 |
| Date | January 2010 |
| Creators | Wu, Kung-Chien, 吳恭儉 |
| Contributors | Lin, Chi-Kun, 林琦焜 |
| Source Sets | National Digital Library of Theses and Dissertations in Taiwan |
| Language | en_US |
| Detected Language | English |
| Type | 學位論文 ; thesis |
| Format | 52 |
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