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arXiv · 1607.02862

A bifurcation analysis for the Lugiato-Lefever equation

Cyril Godey
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Abstract

The Lugiato-Lefever equation is a cubic nonlinear Schrödinger 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.

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Cyril Godey. 2016-07-11. A bifurcation analysis for the Lugiato-Lefever equation. https://doi.org/10.1140/epjd%2Fe2017-80057-2

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