Novel Deformation Function Creating or Destroying any Number of Even Kink Solutions

TL;DR

This paper introduces a novel deformation function that can generate or eliminate multiple kink solutions in scalar field potentials, revealing new invariances and behaviors in kink dynamics.

Contribution

The authors develop a one-parameter deformation function that can produce or destroy any even number of kink solutions in scalar field potentials, expanding the understanding of kink solution manipulation.

Findings

Deformation function is its own inverse.

Certain potentials remain invariant under the deformation.

Deformation can create or annihilate multiple kink solutions.

Abstract

We present a one-parameter family of deformation functions $f(\phi)$ which have novel properties. Firstly, the deformation function is its own inverse. We show that a class of potentials remains invariant under this deformation. Further, when applied to a certain class of kink bearing potentials, one obtains potentials which are not bounded from below. Besides, we show that there is a wide class of potentials having power law kink tails which are connected by this deformation but the corresponding kink tails of the two potentials have different asymptotic behavior. Finally, we show that when this deformation function is applied to an appropriate one-parameter family of potentials having two kink solutions, it creates new potentials with an arbitrary even number ($2n$) of kink solutions. Conversely, by starting from this potential with $2n$ kink solutions the deformation function annihilates $2n-2$ kinks and we get back the potential which we started with having only two kink solutions.