Dissipative solitons with extreme spikes in the normal and anomalous dispersion regimes

N Akhmediev; J M Soto-Crespo; Peter Vouzas; N Devine; Wonkeun Chang

doi:10.1098/rsta.2018.0023

Dissipative solitons with extreme spikes in the normal and anomalous dispersion regimes

Philos Trans A Math Phys Eng Sci. 2018 Jul 28;376(2124):20180023. doi: 10.1098/rsta.2018.0023.

Authors

N Akhmediev¹, J M Soto-Crespo², Peter Vouzas³, N Devine³, Wonkeun Chang⁴

Affiliations

¹ Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Acton ACT 2601, Australia nna124@rsphysse.anu.edu.au.
² Instituto de Óptica, C.S.I.C., Serrano 121, 28006 Madrid, Spain.
³ Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Acton ACT 2601, Australia.
⁴ School of Electrical and Electronic Engineering, College of Engineering, Nanyang Technological University, Singapore 639798, Singapore.

Abstract

Prigogine's ideas of systems far from equilibrium and self-organization (Prigogine & Lefever. 1968 J. Chem. Phys.48, 1695-1700 (doi:10.1063/1.1668896); Glansdorff & Prigogine. 1971 Thermodynamic theory of structures, stability and fluctuations New York, NY/London, UK: Wiley) deeply influenced physics, and soliton science in particular. These ideas allowed the notion of solitons to be extended from purely integrable cases to the concept of dissipative solitons. The latter are qualitatively different from the solitons in integrable and Hamiltonian systems. The variety in their forms is huge. In this paper, one recent example is considered-dissipative solitons with extreme spikes (DSESs). It was found that DSESs exist in large regions of the parameter space of the complex cubic-quintic Ginzburg-Landau equation. A continuous variation in any of its parameters results in a rich structure of bifurcations.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

Keywords: Ginzburg–Landau equation; bifurcations; dissipative solitons; extreme spikes; rogue waves.