One-dimensional delocalizing transitions of matter waves in optical lattices

We investigate, both analytically and numerically, the conditions for the occurrence of the delocalizing transition phenomenon of one-dimensional localized modes of several nonlinear continuous periodic and discrete systems of the nonlinear Schrodinger type. We show that either non-existence of solitons in the small amplitude limit or the loss of stability along existence branches can lead to delocalizing transitions, which occur following different scenarios. Examples of delocalizing transitions of both types are provided for a class of equations which describe single component and binary mixtures of Bose-Einstein condensates trapped in linear and nonlinear optical lattices.