On modified scattering for 1D quadratic Klein-Gordon equations with non-generic potentials
Abstract
We consider the asymptotic behavior of small global-in-time solutions to a 1D Klein-Gordon equation with a spatially localized, variable coefficient quadratic nonlinearity and a non-generic linear potential. The purpose of this work is to continue the investigation of the occurrence of a novel modified scattering behavior of the solutions that involves a logarithmic slow-down of the decay rate along certain rays. This phenomenon is ultimately caused by the threshold resonance of the linear Klein-Gordon operator. It was previously uncovered for the special case of the zero potential in [51]. The Klein-Gordon model considered in this paper is motivated by the asymptotic stability problem for kink solutions arising in classical scalar field theories on the real line.
Cite
@article{arxiv.2012.15191,
title = {On modified scattering for 1D quadratic Klein-Gordon equations with non-generic potentials},
author = {Hans Lindblad and Jonas Luhrmann and Wilhelm Schlag and Avy Soffer},
journal= {arXiv preprint arXiv:2012.15191},
year = {2022}
}
Comments
61 pages. Minor Revisions. To appear in IMRN