An exact treatment for the BEC with three-body recombination and time-dependent scattering length

In this study, Gross-Pitaevskii (GP) equation with three-body recombination and with a time-dependent scattering length is investigated. It is shown that GP equation admits an exact solution for a special choice of the time-dependent scattering length. The effect of Feshbach resonance on the collapse dynamics is investigated for large ∣a∣ for which the three body recombination rate K3 grows with a4.