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Orbital stability and spectral properties of solitary waves of Klein-Gordon equation with concentrated nonlinearity. (English) Zbl 1478.35080

Summary: We obtain explicit characterization of orbital and spectral stability of solitary wave solutions to the \(\mathbf{U}(1)\)-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.

MSC:

35C08 Soliton solutions
35B35 Stability in context of PDEs
35L15 Initial value problems for second-order hyperbolic equations
35L71 Second-order semilinear hyperbolic equations
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