Dark solitons in the Lugiato-Lefever equation with normal dispersion

TL;DR

This paper investigates the existence, stability, and bifurcation structure of dark solitons in the Lugiato-Lefever equation with normal dispersion, highlighting their relevance to frequency comb generation in microresonators.

Contribution

It provides a detailed analysis of dark solitons' bifurcation structure and stability in the Lugiato-Lefever model with normal dispersion, advancing understanding of their dynamics.

Findings

Dark solitons are organized in collapsed snaking bifurcation structure.

Regions of multistability for dark solitons are identified.

Dynamical instabilities lead to oscillations and chaos.

Abstract

The regions of existence and stability of dark solitons in the Lugiato-Lefever model with normal chromatic dispersion are described. These localized states are shown to be organized in a bifurcation structure known as collapsed snaking implying the presence of a region in parameter space with a finite multiplicity of dark solitons. For some parameter values dynamical instabilities are responsible for the appearance of oscillations and temporal chaos. The importance of the results for understanding frequency comb generation in microresonators is emphasized.