Nonautonomous solitons in nonlinear optics and Bose-Einstein condensates

We consider the generalized Gross-Pitaevskii models with varying nonlinearities from the point of view of their exact integrability and obtain the general solutions for these models both for confining and expulsive external potentials. We show that exact soliton solutions exist only under certain conditions and that varying in time nonlinearity and confining harmonic potential cannot be chosen independently; they satisfy the exact integrability conditions. The main features of nonautonomous matter-wave solitons near the Feshbach resonance with continuously tuned scattering length are investigated. We focus on the most physically important situations where the applied magnetic field is varying in time linearly and periodically. It is proved that near a Feshbach resonance the matter wave solitons can be stabilized even without a trapping potential. In the case of periodically varying interaction strength among atoms, variations of the external harmonic potential are found to be sign-reversal. The main difference from the canonical soliton case is that the matter-wave solitons management concept must be consistent with variations of confining potential.

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