Collective Oscillations of a Quasi One Dimensional Bose Condensate Under Damping
ABSTRACT 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 (Zh. Eksp. Teor. Fiz. 35:408, 1958a; Sov. Phys. JETP 35:282, 1958b) 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.
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ABSTRACT: The spatial dynamics of pulses in Kerr media with parabolic index profile are examined. It is found that when diffraction and graded-index have opposite signs propagating pulses exhibit an oscillatory pattern, similar to a breathing behavior. Furthermore, if the pulse and the index profile are not aligned the pulse oscillates around the index origin with frequency that depends on the values of the diffraction and index of refraction. These oscillations are not observed when diffraction and graded-index share the same sign.Optics Communications.