Averaging of Nonlinearity Management with Dissipation

My paper called Averaging of nonlinearity management with dissipation just appeared in Physical Review A. My coauthors are S. Beheshti, K. J. H. Law, and P. G. Kevrekidis (all from U. Mass. Amherst).

This paper is a short but interesting bit of research whose motivation is best described with its 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 Schrödinger 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.


Basically, the point is that the theoretical research involving "nonlinearity management" (which typically means using temporal and/or spatial adjustment on one or more of the nonlinear terms in a partial differential equation) uses an entirely conservative setting. However, one one applies one of these strategies experimentally, there is typically an additional dissipation mechanism that gets introduced. (We saw this in our work with experimentalists on nonlinearity management in the setting of nonlinear optics. This short paper was especially motivated by the associated series of experiments, though it's relevant for some Bose-Einstein condensate stuff as well.) Our paper take some theory for the conservative case and works it out for the periodic dissipation case that we saw in our optics experiments as an example of how one would do this more generally.