標題: Singular Limits of the Klein-Gordon Equation
作者: Lin, Chi-Kun
Wu, Kung-Chien
應用數學系
數學建模與科學計算所(含中心)
Department of Applied Mathematics
Graduate Program of Mathematical Modeling and Scientific Computing, Department of Applied Mathematics
公開日期: 1-Aug-2010
摘要: We 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, h -> 0, 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, c -> infinity, of the modulated defocusing nonlinear Klein-Gordon equation is the defocusing nonlinear Schrodinger equation. The nonrelativistic-semiclassical limit, h -> 0, c = h (-alpha) -> infinity for some alpha > 0, of the modulated defocusing cubic nonlinear Klein-Gordon equation is the classical wave map for the limit wave function and a typical linear wave equation for the associated phase function.
URI: http://dx.doi.org/10.1007/s00205-010-0324-8
http://hdl.handle.net/11536/32388
ISSN: 0003-9527
DOI: 10.1007/s00205-010-0324-8
期刊: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
Volume: 197
Issue: 2
起始頁: 689
結束頁: 711
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