Existence of solitary waves in dipolar quantum gases

We study a nonlinear Schrödinger equation arising in the mean field description of dipolar quantum gases. Under the assumption of sufficiently strong dipolar interactions, the existence of standing waves, and hence solitons, is proved together with some of their properties. This gives a rigorous argument for the possible existence of solitary waves in Bose–Einstein condensates, which originate solely due to the dipolar interaction between the particles.

Research highlights
► We study the Gross–Pitaevskii equation for dipolar quantum gases.
► This model takes into accont the direct short range interaction between particles as well as long-range dipolar forces (which in addition, are spatially anisotropic).
► We rigorously prove the existence of solitary waves in such systems.
► In particular we show the existence of dipolar waves which are solely due to the dipolar interactions.
► These solitary waves can not be considered as (small) perturbations of the well known “bright matter wave solitons” due to the direct (i.e. cubically nonlinear) interaction.