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arXiv · 2208.11240

On the NLS approximation for the nonlinear Klein-Gordon equation

Seokchang Hong·Younghun Hong
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Abstract

In this paper, developing a new approach based on Fourier analysis methods for dispersive PDEs, we establish a low regularity NLS approximation for the one-dimensional cubic Klein-Gordon equation. Our main result includes energy class solutions which are formally asymptotically in $L^2(\mathbb{R})$. A precise rate of convergence is also obtained assuming more regularity.

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Seokchang Hong, Younghun Hong. 2022-08-24. On the NLS approximation for the nonlinear Klein-Gordon equation. https://arxiv.org/abs/2208.11240

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