  Many solitonic configurations in field theory have localized bound states in
their spectrum of linear perturbations. This opens up the possibility of having
long lived excitations of these solitons that could affect their dynamics. We
start the study of these effects in the simplest configuration of a domain wall
kink solution in the $\lambda \phi^4$ theory in $1+1$ dimensions. We show that
this solution has a single bound state and numerically study its slow decay
rate in flat space. We then investigate the amplitude of this excitation by
simulating a cosmological phase transition that leads to the formation of these
kinks in an expanding universe. We find that kinks get formed with a $20\%$
excess of energy with respect to their lowest energy configuration. We also
explore the kink solution interacting with a thermal bath and extract the
amplitude of the localized excitation as a function of temperature. We note
that this amplitude increases with temperature but again the extra energy in
the kink never goes over the $20\%$ level. Finally, we argue that this extra
energy may have important consequences in the subsequent evolution of defects
in numerical simulations.
