On spectral and orbital stability for the Klein--Gordon equation coupled to an anharmonic oscillator

Abstract

We obtain explicit characterization of spectral and orbital stability of solitary wave solutions to the $\mathbf{U}(1)$-invariant Klein--Gordon equation in one spatial dimension coupled to an anharmonic oscillator. We also give the complete analysis of the spectrum of the linearization at a solitary wave.

arXiv comment23 pages

References in corpus (2)

• Global attractor for a nonlinear oscillator coupled to the Klein-Gordon field
• Stability of Standing Waves for a Nonlinear Klein-Gordon Equation with Delta Potentials