  We have applied the transformation of the slow light equations to Liouville
theory that we developed in our previous work, to study the influence of
relaxation on the soliton dynamics. We solved the problem of the soliton
dynamics in the presence of relaxation and found that the spontaneous emission
from the upper atomic level is strongly suppressed. Our solution proves that
the spatial shape of the soliton is well preserved even if the relaxation time
is much shorter than the soliton time length. This fact is of great importance
for applications of the slow-light soliton concept in optical information
processing. We also demonstrate that the relaxation plays a role of resistance
to the soliton motion and slows the soliton down even if the controlling field
is constant.
