Domain wall thickness and deformations of the field model

TL;DR

This paper investigates how bounded deformations in field-theoretic models affect the asymptotic behavior and thickness of flat domain wall solutions, showing that exponential and power-law asymptotics are preserved but parameters can change.

Contribution

It demonstrates that bounded deformations alter the parameters of domain wall asymptotics without changing their fundamental exponential or power-law nature.

Findings

Exponential asymptotics remain exponential after deformation.

Power-law asymptotics remain power-law after deformation.

Deformation parameters influence wall thickness.

Abstract

We consider the change in the asymptotic behavior of solutions of the type of flat domain walls (i.e., kink solutions) in field-theoretic models with a real scalar field. We show that when the model is deformed by a bounded deforming function, the exponential asymptotics of the corresponding kink solutions remain exponential, while the power-law ones remain power-law. However, the parameters of these asymptotics, which are related to the wall thickness, can change.