Soliton response to transient trap variations

The response of bright and dark solitons to rapid variations in an expulsive longitudinal trap is investigated. We concentrate on the effect of transient changes in the trap frequency in the form of temporal delta kicks and the hyperbolic cotangent functions. Exact expressions are obtained for the soliton profiles. This is accomplished using the fact that a suitable linear Schrodinger stationary state solution in time can be effectively combined with the solutions of the nonlinear Schrodinger equation, for obtaining solutions of the Gross-Pitaevskii equation with a time-dependent scattering length in a harmonic trap. Interestingly, there is rapid pulse amplification in certain scenarios.