Dissipative solitons: perturbations and chaos formation

TL;DR

This paper analyzes how perturbations affect chirped dissipative solitons in the spectral domain, revealing complex structures, spectral irregularities, and chaos development, including soliton fragmentation while maintaining localization.

Contribution

It provides a detailed spectral analysis of perturbations in dissipative solitons, highlighting the development of chaos and spectral irregularities, which was not previously characterized.

Findings

Spectral perturbations tend to amplify at the spectrum edges.

Perturbed solitons can become chaotic and fragmented.

Spectral irregularities spread across the entire spectrum.

Abstract

The perturbations of chirped dissipative solitons are analyzed in the spectral domain. It is shown, that the structure of the perturbed chirped dissipative soliton is highly nontrivial and has a tendency to an enhancement of the spectral perturbations especially at the spectrum edges, where the irregularities develop. Even spectrally localized perturbations spread over a whole soliton spectrum. As a result of spectral irregularity, the chaotic dynamics develops due to the spectral loss action. In particular, the dissipative soliton can become fragmented though remains localized.