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

Prigogine’s ideas of systems far from equilibrium and self-organization (Prigogine & Lefever. 1968J. Chem. Phys. 48 , 1695–1700 (doi:10.1063/1.1668896 ); Glansdorff & Prigogine. 1971Thermodynamic 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)’.