Scattering of kinks of the sinh-deformed $\varphi^4$ model

TL;DR

This paper investigates the scattering behavior of kinks in the sinh-deformed $^4$ model, revealing velocity-dependent collision outcomes, including reflection, capture, and oscillon formation, with a critical velocity threshold.

Contribution

It introduces the sinh-deformed $^4$ model and analyzes its kink scattering, highlighting new collision regimes and phenomena not previously studied in this deformation context.

Findings

Identification of a critical velocity $v_{cr}$ separating reflection and complex interactions.

Observation of oscillon formation and escape in kink collisions below $v_{cr}$.

Different collision scenarios depending on initial velocity, including capture and escape windows.

Abstract

We consider the scattering of kinks of the sinh-deformed $\varphi^4$ model, which is obtained from the well-known $\varphi^4$ model by means of the deformation procedure. Depending on the initial velocity $v_{in}$ of the colliding kinks, different collision scenarios are realized. There is a critical value $v_{cr}$ of the initial velocity, which separates the regime of reflection (at $v_{in}>v_{cr}$) and that of a complicated interaction (at $v_{in}<v_{cr}$) with kinks' capture and escape windows. Besides that, at $v_{in}$ below $v_{cr}$ we observe the formation of a bound state of two oscillons, as well as their escape at some values of $v_{in}$.