Physics – Condensed Matter – Other Condensed Matter
Scientific paper
2008-12-25
Physics
Condensed Matter
Other Condensed Matter
14 pages, 6 figures
Scientific paper
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 Schr\"odinger equation, sharing with these the propriety of being unstable against small norm (number of atoms) variations. We show that in the 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 Schr\"odinger equation with higher order nonlinearities is also discussed.
Abdullaev Fatkhulla Kh.
Baizakov Bakhtiyor B.
Salerno Mario
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