Abstract

Dissipative solitons with extreme spikes (DSESs), previously thought to be rare solutions of the complex cubic–quintic Ginzburg–Landau equation, occupy in fact a significant region in its parameter space. The variation of any of its five parameters results in a rich structure of bifurcations. We have constructed several bifurcation diagrams that reveal periodic and chaotic dynamics of DSESs. There are various routes to the chaotic behavior of DSESs, including a sequence of period-doubling bifurcations. It is well known that the complex cubic–quintic Ginzburg–Landau equation can serve as a master equation for the description of passively mode-locked lasers. Our results may lead to the observation of DSESs in laser systems.

© 2017 Optical Society of America

Role of the quintic nonlinear refractive term in the stability of dissipative solitons of the complex Ginzburg–Landau equation

Jose M. Soto-Crespo and N. Akhmediev
J. Opt. Soc. Am. B 38(12) 3541-3548 (2021)

Spiny solitons and noise-like pulses

Wonkeun Chang, Jose M. Soto-Crespo, Peter Vouzas, and Nail Akhmediev
J. Opt. Soc. Am. B 32(7) 1377-1383 (2015)

Period-doubling bifurcations of breathing solitons in dissipative systems

Lijun Song, Hongyan Wang, Liang Wu, and Lu Li
J. Opt. Soc. Am. B 28(1) 86-88 (2011)

High-amplitude dissipative solitons in the normal and anomalous dispersion regimes

S. C. Latas and M. F. S. Ferreira
J. Opt. Soc. Am. B 36(11) 3016-3023 (2019)

Influence of external phase and gain-loss modulation on bound solitons in laser systems

Wonkeun Chang, Nail Akhmediev, Stefan Wabnitz, and Majid Taki
J. Opt. Soc. Am. B 26(11) 2204-2210 (2009)