Solitary waves in Bose-condensed atomic clouds with attractive interactions

We discuss the propagation of compact wave packets in a three-dimensional Bose condensate of atoms with attractive interactions, in a regime where the longitudinal coherence length is much larger than the transverse dimensions. Harmonic transverse confinement is assumed and treated dynamically by a method proposed by Jackson, Kavoulakis and Pethick (Phys. Rev. A 58 (1998) 2417). Propagation of solitary waves occurs in this regime in the absence of axial confinement and indeed, starting from a generic initial profile, self-organization of compact wave packets of matter can take place above a threshold. We also discuss the role of a weak axial confinement and illustrate it with numerical calculations on a condensate of Lithium atoms.