Averaging of Nonlinearity Management with Dissipation

TL;DR

This paper derives an averaged nonlinear PDE to model complex field dynamics in a nonlinear Schrödinger system with periodic nonlinearity and dissipation, validated through numerical comparisons with the original model.

Contribution

It introduces a novel averaged equation incorporating dissipation effects, bridging experimental setups with theoretical modeling in nonlinear optics and atomic physics.

Findings

Good agreement between averaged and original models in simulations

Effective modeling of dissipation in nonlinear Schrödinger equations

Potential applications in optical and atomic physics experiments

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 Schroedinger model in the presence of a periodic nonlinearity and a periodically-varying dissipation coefficient. The incorporation of dissipation 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.