Gap-Townes Solitons and Delocalizing Transitions of Multidimensional Bose-Einstein Condensates in Optical Lattices

We show the existence of gap-Townes solitons for the multidimensional Gross-Pitaeviskii equation with attractive interactions and in two- and three-dimensional optical lattices. In absence of the periodic potential the solution reduces to the known Townes solitons of the multi-dimensional nonlinear Schrodinger equation, sharing with these the property of being unstable against small norm (number of atoms) variations. We show that in presence of the optical lattice the solution separates stable localized solutions (gap-solitons) from decaying ones, characterizing the delocalizing transition occurring in the multidimensional case. The link between these higher dimensional solutions and the ones of one dimensional nonlinear Schrodinger equation with higher order nonlinearities is also discussed