Exploding dissipative solitons in the cubic-quintic complex Ginzburg-Landau equation in one and two spatial dimensions

2014 ◽  
Vol 223 (11) ◽  
pp. 2145-2159 ◽  
Author(s):  
C. Cartes ◽  
O. Descalzi ◽  
H.R. Brand
Keyword(s):  
Landau Equation ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Dissipative Solitons ◽  
Spatial Dimensions

scholarly journals SPATIOTEMPORAL CHAOS, LOCALIZED STRUCTURES AND SYNCHRONIZATION IN THE VECTOR COMPLEX GINZBURG–LANDAU EQUATION

1999 ◽  
Vol 09 (12) ◽  
pp. 2257-2264 ◽  
Author(s):  
EMILIO HERNÁNDEZ-GARCÍA ◽  
MIGUEL HOYUELOS ◽  
PERE COLET ◽  
MAXI SAN MIGUEL ◽  
RAÚL MONTAGNE
Keyword(s):  
Chaotic Dynamics ◽  
Landau Equation ◽  
Spatiotemporal Chaos ◽  
Quantitative Characterization ◽  
Ginzburg Landau ◽  
Information Measures ◽  
Localized Structures ◽  
Ginzburg Landau Equation ◽  
Spatial Dimensions

We study the spatiotemporal dynamics, in one and two spatial dimensions, of two complex fields which are the two components of a vector field satisfying a vector form of the complex Ginzburg–Landau equation. We find synchronization and generalized synchronization of the spatiotemporally chaotic dynamics. The two kinds of synchronization can coexist simultaneously in different regions of the space, and they are mediated by localized structures. A quantitative characterization of the degree of synchronization is given in terms of mutual information measures.

ASYMPTOTIC DYNAMICS OF 2D FRACTIONAL COMPLEX GINZBURG–LANDAU EQUATION

2013 ◽  
Vol 23 (12) ◽  
pp. 1350202 ◽  
Author(s):  
HONG LU ◽  
SHUJUAN LÜ ◽  
ZHAOSHENG FENG
Keyword(s):  
Global Attractor ◽  
Landau Equation ◽  
Fractal Dimensions ◽  
Well Posedness ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Spatial Dimensions ◽  
Asymptotic Dynamics ◽  
Hausdorff And Fractal Dimensions ◽  
The Galerkin Method

In this paper, we consider the well-posedness and asymptotic behaviors of solutions of the fractional complex Ginzburg–Landau equation with the initial and periodic boundary conditions in two spatial dimensions. We explore the existence and uniqueness of global smooth solution by means of the Galerkin method and establish the existence of the global attractor. The estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractor are presented.

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).

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