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The stability and collapse of fundamental unstaggered bright solitons in thediscrete Schrodinger equation with the nonpolynomial on-site nonlinearity,which models a nearly one-dimensional Bose-Einstein condensate trapped in adeep optical lattice, are studied in the presence of the long-rangedipole-dipole (DD) interactions. The cases of both attractive and repulsivecontact and DD interaction are considered. The results are summarized in theform of stability/collapse diagrams in the parametric space of the model, whichdemonstrate that the the attractive DD interactions stabilize the solitons andhelp to prevent the collapse. Mobility of the discrete solitons is brieflyconsidered too.

Soliton stability and collapse in the discrete nonpolynomial Schrodinger equation with dipole-dipole interactions