Averaging of nonlinearity management with dissipation
Shabnam BeheshtiDepartment of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USAKody J. H. LawDepartment of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USAP. G. KevrekidisDepartment of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USAMason A. PorterOxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, OX1 3LB, United Kingdom
2008en
ABI
Abstract
Motivated by recent experiments in optics and atomic physics, we derive an averaged nonlinear partial differential equation describing the dynamics of the complex field in a nonlinear Schr\"odinger model in the presence of a periodic nonlinearity and a periodically varying dissipation coefficient. The incorporation of dissipation in our model is motivated by experimental considerations. We test the numerical behavior of the derived averaged equation by comparing it to the original nonautonomous model in a prototypical case scenario and observe good agreement between the two.
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