Stability of Standing Waves for a Nonlinear Klein-Gordon Equation with Delta Potentials
Analysis of PDEs
2019-11-12 v2 Mathematical Physics
math.MP
Abstract
In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish local well-posedness of the Cauchy problem by a fixed point argument. Unlike the unperturbed case, a noteworthy difficulty here arises from the possible non-unitarity of the semigroup generating the corresponding linear evolution. We then show that the equation is Hamiltonian and we establish several stability/instability results for its standing waves. Our analysis relies on a detailed study of the spectral properties of the linearization of the equation, and on the well-known 'slope condition' for orbital stability.
Keywords
Cite
@article{arxiv.1810.04874,
title = {Stability of Standing Waves for a Nonlinear Klein-Gordon Equation with Delta Potentials},
author = {Elek Csobo and François Genoud and Masahito Ohta and Julien Royer},
journal= {arXiv preprint arXiv:1810.04874},
year = {2019}
}