Kinks scattering in deformed $\ddot{I}{†}^6$ model

Abstract

The deformed model $\tilde{\ddot{I}}{†}^{(6)}$ is introduced based on the $\ddot{I}{†}^4$ model using a deformation functional $F[\ddot{I}†]$ 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 $\ddot{I}{†}^4$ potential and some of their characteristics from the $\ddot{I}{†}^6$ 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.

34 pages, 11 figures, Version accepted for publication