  We use the time-dependent mean-field Gross-Pitaevskii equation to study the
formation of a dynamically-stabilized dissipation-managed bright soliton in a
quasi-one-dimensional Bose-Einstein condensate (BEC). Because of three-body
recombination of bosonic atoms to molecules, atoms are lost (dissipated) from a
BEC. Such dissipation leads to the decay of a BEC soliton. We demonstrate by a
perturbation procedure that an alimentation of atoms from an external source to
the BEC may compensate for the dissipation loss and lead to a
dynamically-stabilized soliton. The result of the analytical perturbation
method is in excellent agreement with mean-field numerics. It seems possible to
obtain such a dynamically-stabilized BEC soliton without dissipation in
laboratory.
