A new model with solitary waves: solution, stability and quasinormal modes

TL;DR

This paper constructs and analyzes solitary wave solutions in a 1+1 dimensional scalar field theory, demonstrating their stability and characterizing their quasinormal modes through semi-analytical and numerical methods.

Contribution

It introduces a new solitary wave model with a specific potential and provides a detailed stability analysis including quasinormal mode characterization.

Findings

Solitary wave solutions are stable due to bound states in the effective potential.

Quasinormal modes exhibit damped oscillatory behavior, indicating ringdown.

Time-domain analysis confirms the stability and dynamical properties of the solitary waves.

Abstract

We construct solitary wave solutions in a $1+1$ dimensional massless scalar ($\phi$) field theory with a specially chosen potential $V(\phi)$. The equation governing perturbations about this solitary wave has an effective potential which is a simple harmonic well over a region, and a constant beyond. This feature allows us to ensure the stability of the solitary wave through the existence of bound states in the well, which can be found by semi-analytical methods. A further check on stability is performed through our search for quasi-normal modes (QNM) which are defined for purely outgoing boundary conditions. The time-domain profiles of the perturbations and the parametric variation of the QNM values are presented and discussed in some detail. Expectedly, a damped oscillatory temporal behaviour (ringdown) of the fluctuations is clearly seen through our analysis of the quasi-normal modes.