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arXiv · 1712.03768

Dynamics of the nonlinear Klein-Gordon equation in the nonrelativistic limit, II

Stefano Pasquali
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Abstract

We study the 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 an order-$r$ normalized approximation of NLKG (which corresponds to the NLS at order $r=1$), and prove that when $M=\mathbb{R}^d$, $d \geq 2$, small radiation solutions of the order-$r$ normalized equation approximate solutions of the nonlinear NLKG up to times of order $\mathcal{O}(c^{2(r-1)})$.

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Stefano Pasquali. 2017-12-11. Dynamics of the nonlinear Klein-Gordon equation in the nonrelativistic limit, II. https://arxiv.org/abs/1712.03768

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