Soliton stability in systems of two real scalar fields

In this paper we consider a class of systems of two coupled real scalar fields in bidimensional spacetime, the main motivation being the study of the classical or linear stability of soliton solutions. First, 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. We then follow the standard approach to classical stability to introduce the main steps one needs to obtain the spectra of Schrodinger 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, more general, system and present an investigation that introduces new results and offers a comparison with former investigations.