Abstract
We study kink-antikink collisions in a model which interpolates smoothly between the completely integrable sine-Gordon theory, the ϕ4 model, and a ϕ6-like model with three degenerate vacua. We find a rich variety of behaviours, including integrability breaking, resonance windows with increasingly irregular patterns, and new types of windows near the ϕ6-like regime. False vacua, extra kink modes and kink fragmentation play important roles in the explanations of these phenomena. Our numerical studies are backed up by detailed analytical considerations.
Highlights
Solitons can escape after three or more consecutive collisions, leading to an intricate fractal-like structure of nested multi-bounce windows [13, 14]. These resonance windows are related to the reversible exchange of energy between the translational mode of the φ4 kink and its internal mode [13, 14]
This mechanism can be reasonably well approximated in a truncated model, which takes into account only two dynamical degrees of freedom, the collective coordinates of the kink and the internal mode [13, 15, 19, 20]
As the frequency of the internal mode of a kink is shifted towards the mass threshold, an excitation of this mode may excite the radiative modes of the continuous spectrum, affecting the resonance exchange mechanism
Summary
For all in the interior of this range, the potential has just two global minima, at φ = 0 and φ = 2π, and the model is parametrised in such a way that small perturbations around these true vacua always have mass equal to 1 In addition to these perturbative states, the model has kink and antikink solutions which interpolate between the global minima, the kinks interpolating between φ = 0 at x = −∞ and φ = 2π at x = +∞ and. Stronger deformations of the potential (2.2) significantly affect not just the scattering and the form of the topological solitons, and as the deformation parameter approaches the critical value cr, they become almost decomposed into pairs of subkinks interpolating between the true vacua at φ = 0 and 2π via the false vacuum at φ = π, as shown in figure 2.
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