A geo-numerical approach for the classification of fixed points in the reduced model of the cubic-quintic complex Ginzburg–Landau equation

Optik ◽  
2015 ◽  
Vol 126 (24) ◽  
pp. 5325-5330 ◽  
Author(s):  
A. Aissat ◽  
T. Mohammedi ◽  
B. Alshehri
Keyword(s):  
Fixed Points ◽  
Landau Equation ◽  
Numerical Approach ◽  
Reduced Model ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation

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.

Spiral Solutions of the Two-Dimensional Complex Ginzburg–Landau Equation

2001 ◽  
Vol 35 (2) ◽  
pp. 159-161
Author(s):  
Liu Shi-Da ◽  
Liu Shi-Kuo ◽  
Fu Zun-Tao ◽  
Zhao Qiang
Keyword(s):  
Landau Equation ◽  
Two Dimensional ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation
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