Pérez García, Victor M.. 

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