Impact of High-Order Effects on Soliton Explosions in the Complex Cubic-Quintic Ginzburg-Landau Equation

Abstract

We investigate the impact of higher-order nonlinear and dispersive effects on the dynamics of a single soliton solution in the complex cubic-quintic Ginzburg-Landau equation. Operating in the regime of soliton explosions, we show how the splitting of explosion modes is affected by the interplay of the high order effects (HOEs) resulting in the controllable selection of right-or left-side periodic explosions. In addition, we demonstrate that HOEs induce a series of pulsating instabilities, significantly reducing the stability region of the single soliton solution.

Logic gates on stationary dissipative solitons

“…Remarkably, these different forms of dissipative solitons coexist to each other when the equation coefficients belong to certain regions [14,[17][18][19]27]. Moreover, the basic CGLE can easily be extended to more general models accounting for the impact of such high-order effects as third-order dispersion, fourth-order spectral filtering, self-stepping, and stimulated Raman scattering [28][29][30][31][32] as well as an external control [33,34]. In fact, more specific models have been used to study the turbulent-like intensity * tvr@jlu.edu.cn; tvr@rian.kharkov.ua and polarization rogue waves in a Raman fiber laser [35], stationary solitary pulses in a dual-core fiber laser [36], the interaction of stationary, oscillatory and exploding counter-propagating dissipative solitons [37,38], the existence of stable three-dimensional dissipative localized structures in the output of a laser coupled to a distant saturable absorber [39], the emergence and the stability of temporally localized structures in the output of a semiconductor laser passively mode locked by a saturable absorber in the long-cavity regime [40], and dissipative solitons in Bose-Einstein condensates [41][42][43][44][45][46].…”