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Recently, Nattermann and Pokrovsky [PRL 100, 060402 (2008)] have proposed ascaling approach for studying Bose-Einstein condensates in strongly disorderedtraps. In this paper we implement their scaling argument in the framework ofthe variational method for solving the time dependent Gross-Pitaevskiiequation. We consider atomic gases with both short range s-wave interaction andlong range anisotropic dipolar interaction. The theory is addressed to theregime of strong disorder and weak interactions where the physics is dominatedby the collective pinning due to the disorder. The phenomenon of condensatefragmentation in dipolar gases is also analyzed.

Variational approach for Bose-Einstein condensates in strongly disordered traps