Dissipative solitons in the discrete Ginzburg-Landau equation with saturable nonlinearity

2018 ◽  
Vol 97 (5) ◽  
Author(s):  
Fatkhulla Kh. Abdullaev ◽  
Mario Salerno
Keyword(s):  
Landau Equation ◽  
Ginzburg Landau ◽  
Saturable Nonlinearity ◽  
Ginzburg Landau Equation ◽  
Dissipative Solitons

Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg–Landau equation

2011 ◽  
Vol 28 (10) ◽  
pp. 2314 ◽  
Author(s):  
Denis S. Kharenko ◽  
Olga V. Shtyrina ◽  
Irina A. Yarutkina ◽  
Evgenii V. Podivilov ◽  
Mikhail P. Fedoruk ◽  
...  
Keyword(s):  
Landau Equation ◽  
Parameter Family ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Dissipative Solitons ◽  
Stable Solutions

scholarly journals Transition from non-periodic to periodic explosions

2015 ◽  
Vol 373 (2056) ◽  
pp. 20150114 ◽  
Author(s):  
Carlos Cartes ◽  
Orazio Descalzi
Keyword(s):  
Transmission Lines ◽  
Landau Equation ◽  
Period Doubling ◽  
Higher Order ◽  
Ginzburg Landau ◽  
Equation Modelling ◽  
Ginzburg Landau Equation ◽  
Dissipative Solitons ◽  
Soliton Transmission ◽  
Period Doubling Bifurcations

We show the existence of periodic exploding dissipative solitons. These non-chaotic explosions appear when higher-order nonlinear and dispersive effects are added to the complex cubic–quintic Ginzburg–Landau equation modelling soliton transmission lines. This counterintuitive phenomenon is the result of period-halving bifurcations leading to order (periodic explosions), followed by period-doubling bifurcations (or intermittency) leading to chaos (non-periodic explosions).

Stability of Dissipative Solitons as Solutions of Asymmetrical Complex Cubic-quintic Ginzburg-Landau Equation

PIERS Online ◽  
2007 ◽  
Vol 3 (1) ◽  
pp. 83-86
Author(s):  
Vladimir Skarka ◽  
N. B. Aleksic ◽  
D. Gauthier ◽  
D. V. Timotijevic
Keyword(s):  
Landau Equation ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Dissipative Solitons

The transition to explosive solitons and the destruction of invariant tori

Open Physics ◽  
2012 ◽  
Vol 10 (3) ◽  
Author(s):  
Jaime Cisternas ◽  
Orazio Descalzi ◽  
Carlos Cartes
Keyword(s):  
Fixed Points ◽  
Landau Equation ◽  
Invariant Tori ◽  
Frequency Locking ◽  
Linear Dispersion ◽  
Ginzburg Landau ◽  
Chaotic Region ◽  
Ginzburg Landau Equation ◽  
Dissipative Solitons

AbstractWe investigate the transition to explosive dissipative solitons and the destruction of invariant tori in the complex cubic-quintic Ginzburg-Landau equation in the regime of anomalous linear dispersion as a function of the distance from linear onset. Using Poncaré sections, we sequentially find fixed points, quasiperiodicity (two incommesurate frequencies), frequency locking, two torus-doubling bifurcations (from a torus to a 2-fold torus and from a 2-fold torus to a 4-fold torus), the destruction of a 4-fold torus leading to non-explosive chaos, and finally explosive solitons. A narrow window, in which a 3-fold torus appears, is also observed inside the chaotic region.

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