A bifurcation analysis for the Lugiato-Lefever equation
Analysis of PDEs
2017-08-02 v1
Abstract
The Lugiato-Lefever equation is a cubic nonlinear Schr\"odinger equation, including damping, detuning and driving, which arises as a model in nonlinear optics. We study the existence of stationary waves which are found as solutions of a four-dimensional reversible dynamical system in which the evolutionary variable is the space variable. Relying upon tools from bifurcation theory and normal forms theory, we discuss the codimension 1 bifurcations. We prove the existence of various types of steady solutions, including spatially localized, periodic, or quasi-periodic solutions.
Cite
@article{arxiv.1607.02862,
title = {A bifurcation analysis for the Lugiato-Lefever equation},
author = {Cyril Godey},
journal= {arXiv preprint arXiv:1607.02862},
year = {2017}
}