  The results on the behavior of phase-slip centers in thin superconducting
wires based on finite-element modeling and time-dependent Ginzburg-Landau
(TDGL) equations are discussed. For closer relationship with experiments, we
used finite-gap formulation of the TDGL system. Both the dynamic equation for
the Cooper-pair condensate wave-function and the expression for the electric
current are more complex than in the gapless case. On this basis, the influence
of nonequilibrium phonons is explored. These phonons can essentially change the
location of geometrical points in which the phase slippage takes place. They
also affect the frequency of phase-slip oscillations. The reported effects are
experimentally detectable and can be used in practical devices.
