Dynamics of Phi^4 Kinks on a Class of Space Dependent Potentials

TL;DR

This paper investigates the behavior of phi^4 kinks in smooth, space-dependent potentials, analyzing how different potential shapes affect kink dynamics and comparing numerical and theoretical critical velocities.

Contribution

It introduces a two-parameter family of potentials affecting phi^4 kink dynamics and provides a detailed comparison between numerical and theoretical critical velocities.

Findings

Critical velocities depend on potential parameters.

Trajectories illustrate kink interactions with barriers and wells.

Numerical results align with theoretical predictions.

Abstract

In this paper we study the dynamics of $\varphi^{4}$ kinks, generated by considering a particular argument of $\varphi^{4}$ field, in the presence of class of smooth space dependent potentials ie. barriers and wells. Various type of these potentials are produced via two-parameter family. These parameters control the shapes, widths and heights of such potentials. The dynamics are presented through the plotting of the trajectories. We compare numerical calculated critical velocities to theoretical calculations.