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

TL;DR

This paper investigates how long-range dipole-dipole interactions influence the stability and collapse of bright solitons in a discrete nonlinear Schrödinger model relevant to Bose-Einstein condensates in optical lattices, revealing stabilization effects.

Contribution

It introduces analysis of dipole-dipole interactions in the discrete nonpolynomial Schrödinger equation, showing their role in stabilizing solitons and preventing collapse, which is a novel insight.

Findings

Attractive DD interactions stabilize solitons.

DD interactions help prevent collapse.

Stability diagrams map parameter space effects.

Abstract

The stability and collapse of fundamental unstaggered bright solitons in the discrete Schrodinger equation with the nonpolynomial on-site nonlinearity, which models a nearly one-dimensional Bose-Einstein condensate trapped in a deep optical lattice, are studied in the presence of the long-range dipole-dipole (DD) interactions. The cases of both attractive and repulsive contact and DD interaction are considered. The results are summarized in the form of stability/collapse diagrams in the parametric space of the model, which demonstrate that the the attractive DD interactions stabilize the solitons and help to prevent the collapse. Mobility of the discrete solitons is briefly considered too.