Autoresonant generation of solitons in Bose-Einstein condensates by modulation of the interaction strength

The autoresonant approach to generation of solitary structures in Bose-Einstein condensates by chirped frequency space-time modulation of the interaction strength is proposed. Both a spatially periodic case and a finite-size trap are studied numerically within a Gross-Pitaevskii equation. Weakly nonlinear theory of the process is developed in the spatially periodic case using Whitham's averaged variational principle. The theory also describes the threshold phenomenon setting the lowest bound on the amplitude of modulations of the interaction strength for autoresonant excitation.