  The universal theory of weakly nonlinear wave packets given by the nonlinear
Schr\"odinger equation is revisited. In the limit where the group and phase
velocities are very close together, a multiple scale analysis carried out
beyond all orders reveals that a single soliton, bright or dark, can travel at
a different speed than the group velocity. In an exponentially small but finite
range of parameters, the envelope of the soliton is locked to the rapid
oscillations of the carrier wave. Eventually, the dynamics is governed by an
equation anologous to that of a pendulum, in which the center of mass of the
soliton is subjected to a periodic potential. Consequently, the soliton speed
is not constant and generally contains a periodic component. Furthermore, the
interaction between two distant solitons can in principle be profoundly altered
by the aforementioned effective periodic potential and we conjecture the
existence of new bound states. These results are derived on a wide class of
wave models and in such a general way that they are believed to be of universal
validity.
