Plain and oscillatory solitons of the cubic complex Ginzburg-Landau equation with nonlinear gradient terms

• Type: Article in International Scientific Journal
• Date: 2017

Authors

Facao, M (Author) Other; Maria Inês Barbosa de Carvalho (Author) FEUP

Journal

Title: Physical review. E

Vol. 96

ISSN: 2470-0045

Publisher: American Physical Society

Indexing

ISI Web of Knowledge - 8 Citations

Scopus - 10 Citations

Other information

Authenticus ID: P-00N-6FR

DOI: 10.1103/physreve.96.042220

Abstract (EN): In this work, we present parameter regions for the existence of stable plain solitons of the cubic complex Ginzburg-Landau equation (CGLE) with higher-order terms associated with a fourth-order expansion. Using a perturbation approach around the nonlinear Schrdinger equation soliton and a full numerical analysis that solves an ordinary differential equation for the soliton profiles and using the Evans method in the search for unstable eigenvalues, we have found that the minimum equation allowing these stable solitons is the cubic CGLE plus a term known in optics as Raman-delayed response, which is responsible for the redshift of the spectrum. The other favorable term for the occurrence of stable solitons is a term that represents the increase of nonlinear gain with higher frequencies. At the stability boundary, a bifurcation occurs giving rise to stable oscillatory solitons for higher values of the nonlinear gain. These oscillations can have very high amplitudes, with the pulse energy changing more than two orders of magnitude in a period, and they can even exhibit more complex dynamics such as period-doubling.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 9