J Cuevas, BA Malomed, PG Kevrekidis and DJ Frantzeskakis (pdf copy 373 Kb.)
We study families of one-dimensional matter-wave solitons supported by the competition of contact and dipole-dipole (DD) interactions of opposite signs. Soliton families are found, and their stability is investigated in the free space, and in the presence of an optical lattice (OL). Free-space solitons may exist with an arbitrarily weak local attraction if the strength of the DD repulsion is fixed. In the case of the DD attraction, solitons do not exist beyond a maximum value of the local-repulsion strength. In the system which includes the OL, a stability region for subfundamental solitons (SFSs) is found in the second finite bandgap. For the existence of gap solitons (GSs) under the attractive DD interaction, the contact repulsion must be strong enough. In the pposite case, GSs exist if the contact attraction is not too strong. Collisions between solitons in the free space are studied too. In the case of the local attraction, the solitons merge or pass through each other at small and large velocities, respectively. In the opposite case, slowly moving solitons bounce from each other.
Physical Review A 79 (2009) 053608.