Exploring the stability and dynamics of dipolar matter-wave dark solitons

We study the stability, form, and interaction of single and multiple dark solitons in quasi-one-dimensional dipolar Bose-Einstein condensates. The solitons are found numerically as stationary solutions in the moving frame of a nonlocal Gross Pitaevskii equation and characterized as a function of the key experimental parameters, namely the ratio of the dipolar atomic interactions to the van der Waals interactions, the polarization angle, and the condensate width. The solutions and their integrals of motion are strongly affected by the phonon and roton instabilities of the system. Dipolar matter-wave dark solitons propagate without dispersion and collide elastically away from these instabilities, with the dipolar interactions contributing an additional repulsion or attraction to the soliton-soliton interaction. However, close to the instabilities, the collisions are weakly dissipative.