Suppression of two-bounce windows in kink-antikink collisions

TL;DR

This paper investigates how deforming a $$ kink in a topological defect model affects kink-antikink collision dynamics, notably suppressing and reemerging two-bounce windows through vibrational mode interactions.

Contribution

It demonstrates that increasing deformation in the model suppresses two-bounce windows, providing a counterexample to the standard resonant mechanism, and explores non-standard reemergence of these windows.

Findings

Two-bounce windows are suppressed with increased deformation.

Multiple vibrational modes influence the collision dynamics.

Reemergence of two-bounce windows occurs with non-standard structures.

Abstract

We consider a class of topological defects in $(1,1)$-dimensions with a deformed $\phi^4$ kink structure whose stability analysis leads to a Schr\"odinger-like equation with a zero-mode and at least one vibrational (shape) mode. We are interested in the dynamics of kink-antikink collisions, focusing on the structure of two-bounce windows. For small deformation and for one or two vibrational modes, the observed two-bounce windows are explained by the standard mechanism of a resonant effect between the first vibrational and the translational modes. With the increasing of the deformation, the effect of the appearance of more than one vibrational mode is the gradual disappearance of the initial two-bounce windows. The total suppression of two-bounce windows even with the presence of a vibrational mode offers a counterexample from what expected from the standard mechanism. For even larger deformation, some two-bounce windows reappear, but with a non-standard structure.