Exploding soliton and front solutions of the complex cubic–quintic Ginzburg–Landau equation

Abstract

We present a study of exploding soliton and front solutions of the complex cubic-quintic Ginzburg-Landau (CGLE) equation. We show that exploding fronts occur in a region of the parameter space close to that where exploding solitons exist. Explosions occur when eigenvalues in the linear stability analysis for the ground-state stationary solitons have positive real parts. We also study transition from exploding fronts to exploding solitons and observed extremely asymmetric soliton explosions.

Soliton amplification in gain medium governed by Ginzburg–Landau equation

“…5) Different from the so-called "exploding solitons," found in numerical simulations [47,48] and experimentally confirmed in a passively mode-locked solid laser [49], our research indicates that the soliton amplification is continuous with the increase of z. The exploding solitons explode at a certain point, break down into multiple pieces, and subsequently recover their original shape [50]. However, in this paper, the soliton can be amplified continuously and stably, which can be confirmed by expanding the range of z (from 0 to 400, see Fig.…”

Two-dimensional structures in the quintic Ginzburg–Landau equation

“…The following results contain two interesting features: pulsations and transitions between stable and unstable states. As it was explained in [43], a soliton with a very interesting pulsating behavior was discovered for a slightly asymmetric initial shape which is also Gaussian with amplitude A 0 = 5, and widths σ x = 0.8333 and σ y = 0.9091, see Fig. 3, for the set of parameters of row 2 of Table I.…”

“…9. As it has been shown in [43], this class may be unstable and leads to chaos. We also noticed that for the same set of parameters, the beams stop splitting and the soliton appears to be stable.…”

“…This class was first mentioned in [5,36,43,45,46], and later by others [15,[19][20][21], and [14] for symmetric and asymmetric transients. For this class we include a sample of how the simulations sets look like.…”

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

“…In this regime, a localized pulse circulating in the cavity experiences an abrupt structural collapse at certain points of its time evolution and subsequently recovers its original shape. Many numerical studies were reported in this framework [3][4][5][6][7][8][9]. Among the reported features is the stable existence of symmetric and asymmetric explosive localized states (LSs) over a wide range of parameters.…”