# Dynamics of the nonlinear Klein–Gordon equation in the nonrelativistic limit

@article{Pasquali2017DynamicsOT,
title={Dynamics of the nonlinear Klein–Gordon equation in the nonrelativistic limit},
author={Stefano Pasquali},
journal={Annali di Matematica Pura ed Applicata (1923 -)},
year={2017},
volume={198},
pages={903-972}
}
• S. Pasquali
• Published 5 March 2017
• Mathematics
• Annali di Matematica Pura ed Applicata (1923 -)
We study the nonlinear Klein–Gordon (NLKG) equation on a manifold M in the nonrelativistic limit, namely as the speed of light c tends to infinity. In particular, we consider a higher-order normalized approximation of NLKG (which corresponds to the NLS at order $$r=1$$r=1) and prove that when M is a smooth compact manifold or $$\mathbb {R}^d$$Rd, the solution of the approximating equation approximates the solution of the NLKG locally uniformly in time. When $$M=\mathbb {R}^d$$M=Rd, $$d \ge 2$$d…
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