Resonance structures in coupled two-component $\phi^4$ model

TL;DR

This paper numerically investigates kink-antikink collisions in a coupled two-component $$ model, revealing complex resonance structures, new soliton solutions, and fractal collision patterns influenced by internal vibrational modes.

Contribution

It introduces new double kink and kink-non-topological soliton solutions and analyzes their collision dynamics, including resonance structures and stability conditions, in a coupled $$ model.

Findings

Discovery of double kink and lump bound states.

Identification of fractal resonance structures in collisions.

Unstable double kinks for negative coupling constants.

Abstract

We present a numerical study of the process of the kink-antikink collisions in the coupled one-dimensional two-component $\phi^4$ model. Our results reveal two different soliton solutions which represent double kink configuration and kink-non-topological soliton (lump) bound state. Collision of these solitons leads to very reach resonance structure which is related to reversible energy exchange between the kinks, non-topological solitons and the internal vibrational modes. Various channels of the collisions are discussed, it is shown there is a new type of self-similar fractal structure which appears in the collisions of the relativistic kinks, there the width of the resonance windows increases with the increase of the impact velocity. An analytical approximation scheme is discussed in the limit of the perturbative coupling between the sectors. Considering the spectrum of linear fluctuations around the solitons we found that the double kink configuration is unstable if the coupling constant between the sectors is negative.