Theoretical studies of ultrashort-soliton propagation in nonlinear optical media from a general quantum model

We overview some recent theoretical studies of dynamical models beyond the framework of slowly varying envelope approximation, which adequately describe ultrashort-soliton propagation in nonlinear optical media. A general quantum model involving an arbitrary number of energy levels is considered. Model equations derived by rigorous application of the reductive perturbation formalism are presented, assuming that all transition frequencies of the nonlinear medium are either well above or well below the typical wave frequency. We briefly overview (a) the derivation of a modified Korteweg-de Vries equation describing the dynamics of few-cycle solitons in a centrosymmetric nonlinear optical Kerr (cubic) type material, (b) the analysis of a coupled system of Korteweg-de Vries equations describing ultrashort-soliton propagation in quadratic media, and (c) the derivation of a generalized double-sine-Gordon equation describing the dynamics of few-cycle solitons in a generic optical medium. The significance of the obtained results is discussed in detail