  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.
