Highly interactive kink solutions

TL;DR

This paper introduces a new class of real scalar field models with strongly interactive kink solutions exhibiting power-law asymptotics, analyzing their interactions and stability with potential physical applications.

Contribution

It presents a novel class of scalar field models with unique power-law kink solutions, including their interaction dynamics and stability analysis.

Findings

Kink solutions show power-law asymptotics instead of exponential.

Interaction forces between kinks and anti-kinks are characterized analytically and numerically.

Stability analysis reveals resonance peaks despite the absence of bound states.

Abstract

In this work we present a new class of real scalar field models admitting strongly interactive kink solutions. Instead of the usual exponential asymptotic behavior these topological solutions exhibit a power-law one. We investigate the interaction force between a pair of kink/anti-kink solutions both analytically and numerically, by integrating the time dependent field equations of the model. Furthermore, working within the first-order framework, we analyze the linear stability of these solutions. The stability analysis leads to Sch\"odinger-like equations with potentials which, despite admitting no bound states, lead to strong resonance peaks. We argue that these properties are important for some possible physical applications.