Orbital stability and spectral properties of solitary waves of Klein–Gordon equation with concentrated nonlinearity

Abstract

We obtain explicit characterization of orbital and spectral stability of solitary wave solutions to the \begin{document}$ {\bf{U}}(1) $\end{document} -invariant 1D Klein–Gordon equation coupled to an anharmonic oscillator. We also give the complete analysis of the spectrum of the linearization at a solitary wave.