Averaging For Solitons With Nonlinearity Management

We develop an averaging method for solitons of the nonlinear Schr{\"o}dinger equation with periodically varying nonlinearity coefficient. This method is used to effectively describe solitons in Bose-Einstein condensates, in the context of the recently proposed and experimentally realizable technique of Feshbach resonance management. Using the derived local averaged equation, we study matter-wave bright and dark solitons and demonstrate a very good agreement between solutions of the averaged and full equations.