Anomalous resonance phenomena of solitary waves with internal modes

TL;DR

This paper studies how nonlinear Klein-Gordon solitary waves with internal modes respond to external ac driving, revealing resonance phenomena that lead to chaotic motion and depend on the driving frequency relative to the internal mode.

Contribution

It demonstrates the resonance behavior of solitary waves with internal modes under ac driving, highlighting the indirect coupling mechanism and the resulting chaotic dynamics.

Findings

Strong resonance at half the internal mode frequency

Weaker resonance at the internal mode frequency, disappearing with damping

Chaotic motion of the kink center of mass at resonance

Abstract

We investigate the non-parametric, pure ac driven dynamics of nonlinear Klein-Gordon solitary waves having an internal mode of frequency $\Omega_i$. We show that the strongest resonance arises when the driving frequency $\delta=\Omega_i/2$, whereas when $\delta=\Omega_i$ 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.