Deformations of Kink Tails

TL;DR

This paper investigates how deformation procedures affect the asymptotic behavior and stability of kinks in field theories, revealing conditions under which their properties change or remain invariant.

Contribution

It demonstrates that deformation can alter or preserve kink asymptotics, including implicit kinks, and analyzes the impact on stability potential and physical properties.

Findings

Deformation can change kink asymptotics depending on the deforming function.

Stability potential decreases as inverse square for power-law tails.

Deformation affects kink mass and kink-antikink force behavior.

Abstract

We study the asymptotic properties of kinks in connection with the deformation procedure. We show that, upon deformation of the field-theoretic model, the asymptotics of kinks can change or remain unchanged, depending on the properties of the deforming function. The cases of both explicit and implicit kinks are considered. In addition, we show that the the deformation procedure can be applied to the important case of implicit kinks. We also prove that for any kink with a power-law tail, the stability potential decreases as the inverse square of the coordinate. The physical consequences of the deformation are discussed: the change of the kink mass, as well as the asymptotic behavior of the kink-antikink force.