The bifurcation of internal modes from the phonon band in models supporting
solitary wave solutions is currently one of the exciting phenomena in the
held. We will present a number of analytical and semianalytical techniques
for the detection, study, and understanding of these modes. We will see how
they appear, without threshold, due to the discretization of the continuum
equations. This perturbation is viewed in terms of a singular continuum ap
proximation and analyzed by both perturbation theory and the Evans's functi
on method. It is shown that these methods give equivalent results. Moreover
, they are corroborated by mixed analytical-numerical computations based on
the recently developed discrete Evans's function method. The extent to whi
ch these predictions survive to strong discretizations is discussed. The re
sults will be presented in the context of both the sine-Gordon and the phi(
4) models.