A "metaphorical" nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates

We demonstrate the stabilization of two-dimensional nonlinear wave patterns by means of a dissipative confinement potential. Our analytical and numerical analysis, based on the generalized dissipative Gross-Pitaevskii equation, makes use of the close analogy between the dynamics of a Bose-Einstein condensate and that of mode-locked fiber laser, operating in the anomalous dispersion regime. In the last case, the formation of stable two-dimensional patterns corresponds to spatiotemporal mode locking, using dissipation-enhanced mode cleaning. We analyze the main scenarios of pattern destabilization, varying from soliton dissolution to its splitting and spatiotemporal turbulence, and their dependence on graded dissipation.