Hamiltonian averaging for solitons with nonlinearity management

We revisit the averaged equation, derived in Phys. Rev. Lett. 91, 240201 (2003)] from the nonlinear Schrödinger (NLS) equation with the nonlinearity management. We show that this averaged equation is valid only at the initial time interval, while a new Hamiltonian averaged NLS equation can be used at longer time intervals. Using the new averaged equation, we construct numerically matter-wave solitons in the context of the Bose-Einstein condensates under the Feshbach resonance management. We show that there is no threshold on the existence of dark solitons of large amplitudes, whereas such a threshold exists for bright solitons.