Kinks scattering in deformed $\varphi^6$ model

TL;DR

This paper introduces a deformed $ ilde{ ext{phi}}^{(6)}$ model based on the $ ext{phi}^4$ model, analyzes kink solutions and their internal modes, and studies kink-antikink scattering dynamics influenced by a deformation parameter.

Contribution

It presents a new deformed $ ilde{ ext{phi}}^{(6)}$ model, explores its kink solutions and internal modes, and investigates scattering phenomena with variable initial conditions and deformation parameters.

Findings

Kinks inherit properties from both $ ext{phi}^4$ and $ ext{phi}^6$ models.

Critical velocity depends on the deformation parameter.

Unique scattering phenomena occur due to mass differences among sectors.

Abstract

The deformed model $\tilde{\varphi}^{(6)}$ is introduced based on the $\varphi^4$ model using a deformation functional $F[\varphi]$ including a free parameter $a$. The kink solutions in different sectors and their internal modes are obtained as functions of the deformation parameter and their characteristics are evaluated as well. It is shown that the kinks of the deformed model inherit some of their dynamical properties (like internal modes) from the standard $\varphi^4$ potential and some of their characteristics from the $\varphi^6$ model. The dynamics of kink-antikink (antikink-kink) scattering is investigated in different sectors with various kink initial conditions as well as different values of deformation parameter. According to the kinks' initial velocity, colliding kinks may be bound together or scatter from each other after the interaction. These two situations are distinguished by the critical velocity, which itself depends on the deformation parameter of the model. Due to the difference in the rest mass of kink solutions related to different sectors, interesting and sometimes rare phenomena are observed during the kink scattering and their interactions.