Averaging of nonlinearity-managed pulses

Vadim Zharnitsky, Dmitry Pelinovsky
2005 Chaos  
We consider the nonlinear Schrödinger equation with the nonlinearity management which describes Bose-Einstein condensates under Feshbach resonance. By using an averaging theory, we derive the Hamiltonian averaged equation and compare it with other averaging methods developed for this problem. The averaged equation is used for analytical approximations of nonlinearity-managed solitons. We have systematically categorized the averaging procedure for the nonlinear Schrödinger ( NLS) equation with
more » ... LS) equation with nonlinearity management. We have derived an averaged equation by using four equivalent methods: (i) nearidentity canonical transformations, (ii) asymptotic multiscale expansion methods based on local transformations, (iii) asymptotic multi-scale expansion methods based on nonlocal transformations, and (iv) direct perturbation series expansions. Stationary solutions of the averaged equation are used to approximate time-dependent solutions of the full NLS equation. Two families of stationary solutions include bright and dark solitons. We show that these solutions exist in an open quadrant of the parameter plane "␥ 0 , ..., where ␥ 0 is the averaged nonlinearity coefficient and is the frequency of the stationary solutions. 037105-3 Averaging of nonlinearity-managed pulses Chaos 15, 037105 ͑2005͒ Downloaded 02 Nov 2005 to Redistribution subject to AIP license or copyright, see http://chaos.aip.org/chaos/copyright.jsp 037105-6 V. Zharnitsky and D. Pelinovsky Chaos 15, 037105 ͑2005͒
doi:10.1063/1.1922660 pmid:16253000 fatcat:l53wypc5nvdrhiav2qzb3ivdam