Soliton solutions of 3D Gross-Pitaevskii equation by a potential control method

Details Soliton solutions of 3D Gross-Pitaevskii equation by a potential control method Soliton solutions of 3D Gross-Pitaevskii equation by a potential control method

2009-07-09

arxiv.org/abs/0907.1595v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages, 5 figures, submitted to Phys. Rev. E

Scientific paper

We present a class of three-dimensional solitary waves solutions of the Gross-Pitaevskii (GP) equation, which governs the dynamics of Bose-Einstein condensates (BECs). By imposing an external controlling potential, a desired time-dependent shape of the localized BEC excitation is obtained. The stability of some obtained localized solutions is checked by solving the time-dependent GP equation numerically with analytic solutions as initial conditions. The analytic solutions can be used to design external potentials to control the localized BECs in experiment.

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