Rosen-Morse potential and gravitating kinks

TL;DR

This paper constructs kink solutions in a two-dimensional dilaton-gravity-scalar model with noncanonical kinetic terms, leading to Schrödinger-like perturbation equations with Rosen-Morse potentials, revealing diverse stability properties.

Contribution

It introduces a novel class of kink solutions with Rosen-Morse potential perturbations in a specialized dilaton-gravity-scalar framework, utilizing shape invariance for eigenvalue analysis.

Findings

Eigenvalues and wave functions derived analytically.

Stability potential can be reflective or reflectionless.

Zero mode is always absent.

Abstract

We show that in a special type of two-dimensional dilaton-gravity-scalar model, where both the dilaton and the scalar matter fields have noncanonical kinetic terms, it is possible to construct kink solutions whose linear perturbation equation is a Schr\"odinger-like equation with Rosen-Morse potential. For this potential, eigenvalues and wave functions of the bound states, if had any, can be derived by using the standard shape invariance procedure. Depending on the values of the parameters, the stability potential can be reflective or reflectionless. There can be an arbitrary number of shape modes, but the zero mode is always absent.