On Modified Scattering for 1D Quadratic Klein-Gordon Equations With Non-Generic Potentials Academic Article

abstract

• Abstract We consider the asymptotic behavior of small global-in-time solutions to a 1D KleinGordon 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 KleinGordon operator. It was previously uncovered for the special case of the zero potential in [51]. The KleinGordon 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.

authors

• Luhrmann, Jonas

published proceedings

• INTERNATIONAL MATHEMATICS RESEARCH NOTICES

author list (cited authors)

• Lindblad, H., Luhrmann, J., Schlag, W., & Soffer, A.

citation count

• 0

complete list of authors

• Lindblad, Hans||Luhrmann, Jonas||Schlag, Wilhelm||Soffer, Avy

publication date

• March 2023

publisher

• Oxford University Press (OUP)  Publisher

published in

• International mathematics research notices  Journal

keywords

• 49 Mathematical Sciences
• 4902 Mathematical Physics

Digital Object Identifier (DOI)

• 10.1093/imrn/rnac010

start page

• 5118

end page

• 5208

volume

• 2023

issue

• 6

URL

• http://dx.doi.org/10.1093/imrn/rnac010