# A model field theory with $(\psi \ln \psi)^2$ potential: Kinks with super-exponential profiles

## TL;DR

This paper introduces a novel (1+1)-dimensional field theory with a $( ext{psi} \, ext{ln} \, ext{psi})^2$ potential, featuring super-exponential kink solutions with unique properties and complex collision behaviors.

## Contribution

It presents the first known example of kinks with super-exponential profiles and tails, expanding the understanding of topological solitons in field theories.

## Key findings

- Discovery of asymmetric super-exponential kink solutions
- Analysis of domain wall interactions and collisions
- Comparison with $ ext{phi}^6$ model and half-kink solutions

## Abstract

We study a (1+1)-dimensional field theory based on $(\psi \ln \psi)^2$ potential. There are three degenerate minima at $\psi = 0$ and $\psi=\pm1$. There are novel, asymmetric kink solutions of the form $\psi = \mp\exp (-\exp(\pm x))$ connecting the minima at $\psi = 0$ and $\psi = \mp 1$. The domains with $\psi = 0$ repel the linear excitations, the waves (e.g. phonons). Topology restricts the domain sequences and therefore the ordering of the domain walls. Collisions between domain walls are rich for properties such as transmission of kinks and particle conversion, etc. To our knowledge this is the first example of kinks with super-exponential profiles and super-exponential tails. Finally, we provide a comparison of these results with the $\phi^6$ model and its half-kink solution.