On the fluid dynamical approximation to thenonlinear Klein-Gordon equation

Chi-Kun Lin; Kung-Chien Wu

doi:10.3934/dcds.2012.32.2233

Article Contents

2012, Volume 32, Issue 6: 2233-2251. Doi: 10.3934/dcds.2012.32.2233

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On the fluid dynamical approximation to the nonlinear Klein-Gordon equation

Chi-Kun Lin^1, and
Kung-Chien Wu^2,

1.
Department of Applied Mathematics and, Center of Mathematical Modeling and Scientiﬁc Computing, National Chiao Tung University, Hsinchu 30010
2.
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge, CB3 OWA

Received: January 31, 2011

Revised: November 30, 2011

Published: May 2012

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Abstract

We study the nonrelativistic, semiclassical and nonrelativistic-semiclassical limits of the (modulated) nonlinear Klein-Gordon equations from its hydrodynamical structure via WKB analysis. The nonrelativistic-semiclassical limit is proved rigorously by modulated energy method.

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Mathematics Subject Classification: 35L05, 35Q60; 76Y05.

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