On The Darboux Bäcklund Transformation of Optical Solitons with Resonant and Nonresonant Nonlinearity

Abstract: 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.