Unidirectional Propagation of an Ultra-Short Electromagnetic Pulse in a Resonant Medium with High Frequency Stark Shift

We consider in the unidirectional approximation the propagation of an ultra short electromagnetic pulse in a resonant medium consisting of molecules characterized by a transition operator with both diagonal and non-diagonal matrix elements. We find the zero-curvature representation of the reduced Maxwell-Bloch equations in the sharp line limit. This can be used to develop the inverse scattering transform method to solve these equations. Finally we obtain two types of exact traveling pulse solutions, one with the usual exponential decay and another with an algebraic decay.Comment: Latex, 10 pages, no figure

Gap-Townes solitons and localized excitations in low dimensional Bose Einstein condensates in optical lattices

We discuss localized ground states of Bose-Einstein condensates in optical lattices with attractive and repulsive three-body interactions in the framework of a quintic nonlinear Schr\"odinger equation which extends the Gross-Pitaevskii equation to the one dimensional case. We use both a variational method and a self-consistent approach to show the existence of unstable localized excitations which are similar to Townes solitons of the cubic nonlinear Schr\"odinger equation in two dimensions. These solutions are shown to be located in the forbidden zones of the band structure, very close to the band edges, separating decaying states from stable localized ones (gap-solitons) fully characterizing their delocalizing transition. In this context usual gap solitons appear as a mechanism for arresting collapse in low dimensional BEC in optical lattices with attractive real three-body interaction. The influence of the imaginary part of the three-body interaction, leading to dissipative effects on gap solitons and the effect of atoms feeding from the thermal cloud are also discussed. These results may be of interest for both BEC in atomic chip and Tonks-Girardeau gas in optical lattices