Sideband evolution of a complex Ginzburg-Landau equation: a three-dimensional dynamical system and its resulting new aperiodic attractor

1994 ◽  
Vol 72 (1-2) ◽  
pp. 48-60 ◽  
Author(s):  
Jiyue J. Li ◽  
Marshall P. Tulin
Keyword(s):  
Dynamical System ◽  
Landau Equation ◽  
Three Dimensional ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Dimensional Dynamical System

scholarly journals A variational formulation for translation and assimilation of coherent structures

2013 ◽  
Vol 20 (5) ◽  
pp. 793-801
Author(s):  
M. Plu
Keyword(s):  
Dynamical System ◽  
Data Assimilation ◽  
Coherent Structures ◽  
Variational Formulation ◽  
Landau Equation ◽  
Variational Data Assimilation ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Ginzburg Landau Equation ◽  
The One

Abstract. The assimilation of observations from teledetected images in geophysical models requires one to develop algorithms that would account for the existence of coherent structures. In the context of variational data assimilation, a method is proposed to allow the background to be translated so as to fit structure positions deduced from images. Translation occurs as a first step before assimilating all the observations using a classical assimilation procedure with specific covariances for the translated background. A simple validation is proposed using a dynamical system based on the one-dimensional complex Ginzburg–Landau equation in a regime prone to phase and amplitude errors. Assimilation of observations after background translation leads to better scores and a better representation of extremas than the method without translation.

Stable Vortex Tori in the Three-Dimensional Cubic-Quintic Ginzburg-Landau Equation

2006 ◽  
Vol 97 (7) ◽  
Author(s):  
D. Mihalache ◽  
D. Mazilu ◽  
F. Lederer ◽  
Y. V. Kartashov ◽  
L.-C. Crasovan ◽  
...  
Keyword(s):  
Landau Equation ◽  
Three Dimensional ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Stable Vortex

scholarly journals Collisions between counter-rotating solitary vortices in the three-dimensional Ginzburg-Landau equation

2008 ◽  
Vol 78 (5) ◽  
Author(s):  
D. Mihalache ◽  
D. Mazilu ◽  
F. Lederer ◽  
H. Leblond ◽  
B. A. Malomed
Keyword(s):  
Landau Equation ◽  
Three Dimensional ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation
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