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A bifurcation analysis for the Lugiato-Lefever equation

  • Cyril GodeyEmail author
Regular Article
Part of the following topical collections:
  1. Topical Issue: Theory and applications of the Lugiato-Lefever Equation

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.

Graphical abstract

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques de BesançonBesançon CedexFrance

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