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

2017/03/05 by Stefano Pasquali, Pasquali, Stefano · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1703.01609

openalex publication_date 2017/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The nonlinear Klein-Gordon (NLKG) equation on a manifold M in the nonrelativistic limit, namely as the speed of light c tends to infinity, is considered. In particular, a higher-order normalized approximation of NLKG (which corresponds to the NLS at order r=1) is constructed, and when M is a smooth compact manifold or ℝ^d it is proved that the solution of the approximating equation approximates the solution of the NLKG locally uniformly in time. When M=ℝ^d, d ≥ 3, it is proved that solutions of the linearized order r normalized equation approximate solutions of linear Klein-Gordon equation up to times of order O(c^2(r-1)) for any r>1.

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• Optimal convergence rates of the Klein-Gordon-Schrödinger system in the nonrelativistic limit

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