Dynamical Stabilization of nonlinear Waves

Dynamics of solitons in the nonlinear media with rapidly varying parameters are investigated. One-dimensonal and two-dimensional nonlinear Schrödinger equations with a periodic modulation in time of the dispersion, the nonlinearity and the linear potential, are considered. As physical applications we study problems: 1) the stabilization of atomic matter soliton in Bose-Einstein condensate (BEC) with a rapidly varying trap potential; 2) the dynamical stabilization of bright soliton in two dimensional BEC by rapidly oscillating atomic scattering length; (the Feshbach resonance or nonlinearity management), 3)the existence of stable two dimensional dispersion-managed soliton.

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