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We study kink-antikink collisions in a model which interpolates smoothlybetween the completely integrable sine-Gordon theory, the $\phi^4$ model, and a$\phi^6$-like model with three degenerate vacua. We find a rich variety ofbehaviours, including integrability breaking, resonance windows withincreasingly irregular patterns, and new types of windows near the$\phi^6$-like regime. False vacua, extra kink modes and kink fragmentation playimportant roles in the explanations of these phenomena. Our numerical studiesare backed up by detailed analytical considerations.

Resonance structures in kink-antikink collisions in a deformed sine-Gordon model