Logarithmic Potential with Super-Super-Exponential Kink Profiles and Tails

TL;DR

This paper introduces a new one-dimensional logarithmic potential model with diverse super-exponential kink profiles and tails, providing analytic solutions, stability analysis, and comparisons with high-order field theories.

Contribution

It presents an analytic model with complex kink solutions and stability properties, expanding understanding of nonlinear field theories with diverse tail behaviors.

Findings

Analytic kink solutions with varied tail behaviors.

Stability analysis shows a gap between zero mode and continuum.

Comparison with high-order polynomial field theories.

Abstract

We consider a novel one dimensional model of a logarithmic potential which has super-super-exponential kink profiles as well as kink tails. We provide analytic kink solutions of the model -- it has 3 kinks, 3 mirror kinks and the corresponding antikinks. While some of the kink tails are super-super-exponential, some others are super-exponential whereas the remaining ones are exponential. The linear stability analysis reveals that there is a gap between the zero mode and the onset of continuum. Finally, we compare this potential and its kink solutions with those of very high order field theories harboring seven degenerate minima and their attendant kink solutions, specifically $\phi^{14}$, $\phi^{16}$ and $\phi^{18}$.