Collective oscillations of a quasi-one-dimensional Bose condensate under damping

Affect of the damping on collective oscillations of a quasi-one-dimensional trapped repulsive Bose gas has been studied. Based on the phenomenological damping approach [L.P. Pitaevskii, Zh. Eksp. Teor. Fiz. 35 (1958) 408, Sov. Phys. JETP 35 (1958) 282] developed by Pitaevskii variational equations for the parameters of the condensate wave function have been derived. Analytical expressions for the condensate parameters in the steady-state have been obtained. Combined effect of the resonant periodical variation of the trap strength and the damping has been shown to change drastically asymptotical behavior of the driven norm oscillations. Bistability in nonlinear oscillations of the condensate under periodic variations of the trap potential is predicted.