Anomalous resonance phenomena of solitary waves with internal modes

Abstract

We investigate the non-parametric, pure ac driven dynamics of nonlinear Klein-Gordon solitary waves having an internal mode of frequency $Ω_i$. We show that the strongest resonance arises when the driving frequency $δ=Ω_i/2$, whereas when $δ=Ω_i$ the resonance is weaker, disappearing for nonzero damping. At resonance, the dynamics of the kink center of mass becomes chaotic. As we identify the resonance mechanism as an {\em indirect} coupling to the internal mode due to its symmetry, we expect similar results for other systems.