  Solitons in nonlinear optics holds a special role both in theoretical and
experimental studies. Several types of evolution equations are seen to govern
different situation of physical relevance. One such is the existence of both
resonant and nonresonant situation in optical fibre. The corresponding
evolution equation was devised by Doktorov et. al., which consists of a forced
NLS equation along with two other equations for population difference and
polarization. Here, we have followed an earlier formulation of Neugebauer for
Darboux-B\"acklund transformation for this coupled systems. This formalism has
the advantage that one can write the N-soliton solution altogether.An important
difference with the usual non-linear system is that all the field variables are
not present in both part of Lax operator. So we are to apply the DT to both
part separately.
