Soliton Stability in Systems of Two Real Scalar Fields

TL;DR

This paper investigates the classical stability of soliton solutions in coupled two-field scalar systems, analyzing spectral properties of associated Schrödinger operators through analytical and comparative methods.

Contribution

It introduces a framework for analyzing soliton stability in coupled scalar fields and provides new analytical results and comparisons for specific systems.

Findings

Spectral analysis of Schrödinger operators reveals stability conditions.

Analytical solutions for specific coupled systems are derived.

Comparison between different systems highlights stability features.

Abstract

In this paper we consider a class of systems of two coupled real scalar fields in bidimensional spacetime, with the main motivation of studying classical or linear stability of soliton solutions. Firstly, we present the class of systems and comment on the topological profile of soliton solutions one can find from the first-order equations that solve the equations of motion. After doing that, we follow the standard approach to classical stability to introduce the main steps one needs to obtain the spectra of Schr\"odinger operators that appear in this class of systems. We consider a specific system, from which we illustrate the general calculations and present some analytical results. We also consider another system, more general, and we present another investigation, that introduces new results and offers a comparison with the former investigations.