Explicit Kink Solutions in Several One-Parameter Family of Higher Order Field Theory Models

TL;DR

This paper introduces several one-parameter families of higher order field theory models that admit explicit kink solutions with either exponential or power-law tails, analyzing their properties and interactions.

Contribution

It presents new explicit kink solutions in higher order models and applies the Manton formalism to estimate forces between kinks and antikinks.

Findings

Models with power-law tails have no gap between zero mode and continuum.

Explicit kink solutions with exponential and power-law tails are derived.

Force estimates between kinks and antikinks are provided.

Abstract

We present several one-parameter family of higher order field theory models some of which admit explicit kink solutions with an exponential tail while others admit explicit kink solutions with a power-law tail. Various properties of these families of kink solutions are examined in detail. In particular for models harboring kink solutions with a power-law tail, we show that there is no gap between the zero mode and the beginning of the continuum in the kink stability potential. Further, by applying the recent Manton formalism, we provide estimates for the kink-kink and antikink-kink acceleration and hence the ratio of the corresponding antikink-kink and kink-kink forces.