Semi-compactness and multiple oscillating pulses in kink scattering

TL;DR

This paper explores the dynamics of asymmetric kinks transitioning from standard to semi-compacton profiles, revealing how increasing the parameter n influences oscillatory behavior and bounce windows in kink-antikink collisions.

Contribution

It introduces a model of asymmetric kinks with a parameter n, analyzing how the transition to semi-compacton structures affects collision dynamics and oscillatory modes.

Findings

Small n values produce one-bounce windows in kink-antikink collisions.

Increasing n leads to oscillatory modes and breaks the bounce window structure.

Two-bounce and two-oscillation windows appear in antikink-kink collisions.

Abstract

In this work we consider model of asymmetric kinks, where the behavior of the solution in one side is different from the other side. Also, the models depend of an integer $n$ and, with the increase of $n$, the constructed kink assumes a hybrid character: a compactlike profile on one side and a kinklike profile on the other side. We investigate numerically the kink-antikink and antikink-kink dynamics, with the aim to understand the effect of the transition of the usual kink to the semi-compacton structure. The kink-antikink process shows the formation of one-bounce windows for small values of $n$. The increase of $n$ favors the breaking this structure and the appearance of oscillatory modes. For antikink-kink collisions we report the appearance of two-bounce windows for small values of the parameter. We also found an intricate structure of two-oscillation windows.