Pulsating and rotating spirals in a delayed feedback diffractive nonlinear optical system
Pattern Formation and Solitons
2021-10-11 v1 Mathematical Physics
math.MP
Abstract
We study spiral waves in a mathematical model of a nonlinear optical system with a feedback loop. Starting from a delayed scalar diffusion equation in a thin annulus with oblique derivative boundary conditions, we shrink the annulus and derive the limiting equation on a circle. Based on the explicitly constructed normal form of the Hopf bifurcation for the one-dimensional delayed scalar diffusion equation, we make predictions about the existence and stability of two-dimensional spirals that we verify in direct numerical simulations, observing pulsating and rotating spiral waves.
Cite
@article{arxiv.1909.02796,
title = {Pulsating and rotating spirals in a delayed feedback diffractive nonlinear optical system},
author = {Stanislav Budzinskiy and Alexander Razgulin},
journal= {arXiv preprint arXiv:1909.02796},
year = {2021}
}
Comments
16 pages, 8 figures