Singularity structure analysis and the complete integrability of the higher order nonlinear Schrödinger-Maxwell-Bloch equations

We propose the coupled system of the generalized nonlinear Schrödinger equation and the Maxwell-Bloch equations, which finds application in nonlinear fiber optics. Using the Painlevé singularity structure analysis, the condition for the complete integrability is obtained. The Lax pair and other properties of the equations are discussed. With suitable parametric conditions, other interesting soliton models are generated.