ON THE FLUID DYNAMICAL APPROXIMATION TO THE NONLINEAR KLEIN-GORDON EQUATION

Lin, Chi-Kun; Wu, Kung-Chien

doi:10.3934/dcds.2012.32.2233

ON THE FLUID DYNAMICAL APPROXIMATION TO THE NONLINEAR KLEIN-GORDON EQUATION

Date

2012-06-01

Authors

Lin, Chi-Kun

Wu, Kung-Chien

DOI

10.3934/dcds.2012.32.2233

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.

Keywords

Nonlinear Klein-Gordon equation , nonlinear Schrodinger equation , semiclassical limit , nonrelativistic limit , nonrelativistic-semiclassical limit , compressible Euler equations , WKB approximation , wave map

URI

http://dx.doi.org/10.3934/dcds.2012.32.2233
https://ir.lib.nycu.edu.tw/handle/11536/15525

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ON THE FLUID DYNAMICAL APPROXIMATION TO THE NONLINEAR KLEIN-GORDON EQUATION

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