Dark solitons in time dependent traps

V. A. Brazhnyi, V. V. Konotop and L. P. Pitaevskii

University of Lisbon, Center of Theoretical and Computational Physics, Lisbon, Portugal

We present a theory of dark soliton dynamics in quasi-one-dimensional Bose-Einstein condensates trapped by time dependent potentials. The theory is based on the local density approximation and is applicable for arbitrary polynomial nonlinearities of the mean-field equation governing the system. We derive a general formula for the frequency of the soliton oscillations in confining potentials. A special attention is dedicated to the study of the soliton dynamics in adiabatically varying traps. Various limiting cases are addressed. In particular, for the slow solitons general formulas for the effective mass and for the frequency of oscillations are obtained.

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