Rotating Waves in a Model of Delayed Feedback Optical System with Diffraction

Abstract

We study a delayed parabolic functional differential equation on a circle that is coupled with an initial value problem for the Schrodinger equation. Such equations arise as models of nonlinear optical systems with a timedelayed feedback loop, when diffusion of molecular excitation and diffraction are taken into account. The goal of this paper is to prove the existence of spatially inhomogeneous rotating-wave solutions bifurcating from homogeneous equilibria. We pass to a rotating coordinate system and seek an inhomogeneous solution to an ordinary functional differential equation. We find the solution in the form of a small parameter expansion and explicitly compute the first-order coefficients. We also provide examples of parameters that satisfy the constraints imposed throughout the analysis.