On Modified Scattering for 1D Quadratic KleinGordon Equations With Non-Generic Potentials Academic Article uri icon

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.

published proceedings

  • International Mathematics Research Notices

author list (cited authors)

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

publication date

  • January 1, 2022 11:11 AM