Bäcklund transformations for the reduced Maxwell-Bloch equations (Q2781683)

The author presents an overview of some recent work done on a two-level reduction of the semi-classical model of the interaction of light with matter. These reduced Maxwell-Bloch (RMB) equations are derived without recourse to the slowly varying envelop approximation (SVEA). The author shows that such reduced equations are completely integrable by deriving a Lax pair for them. Moreover, the author uses the integrable structure to construct Darboux-Bäcklund transformations from which one can deduce the explicit formulae for physically relevant one and two solition solutions.NEWLINENEWLINEFor the entire collection see [Zbl 0974.00040].