Matter-wave solitons supported by dissipation

We show how novel types of long-lived self-localized matter waves can be constructed with Bose-Einstein condensates. The ingredients leading to such structures are a spatial phase generating a flux of atoms towards the condensate center and the dissipative mechanism provided by the inelastic three-body collisions in atomic Bose-Einstein condensates. The outcome is an striking example of nonlinear structure supported by dissipation.