scholarly journals Creeping solitons of the complex Ginzburg–Landau equation with a low-dimensional dynamical system model

2007 ◽  
Vol 362 (1) ◽  
pp. 31-36 ◽  
Author(s):  
Wonkeun Chang ◽  
Adrian Ankiewicz ◽  
Nail Akhmediev
Keyword(s):  
Dynamical System ◽  
Landau Equation ◽  
System Model ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Dimensional Dynamical System ◽  
Low Dimensional

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.

scholarly journals Analysis of the 2D complex Ginzburg-Landau Equation using Singular Value Decomposition

2021 ◽  
Author(s):  
Emily Gottry ◽  
Edwin Ding
Keyword(s):  
Singular Value Decomposition ◽  
Landau Equation ◽  
Singular Value ◽  
Optical Systems ◽  
Qualitative Behavior ◽  
Dimensional Model ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Low Dimensional ◽  
Value Decomposition

The cubic-quintic Ginzburg-Landau equation (CQGLE) governs the dynamics of solitons in lasers and many optical systems. Using data obtained from the simulations of the CQGLE, we performed a singular value decomposition (SVD) to create a low dimensional model that qualitatively predicts the stability of the solitons as a function of the energy gain constant. It was found both in the full simulations and in the low dimensional model that the soliton becomes unstable when the gain exceeds a certain threshold value. Both the low dimensional model and the full simulation demonstrated the same qualitative behavior when the soliton loses stability.

Low-dimensional behaviour in the complex Ginzburg-Landau equation

Nonlinearity ◽  
1988 ◽  
Vol 1 (2) ◽  
pp. 279-309 ◽  
Author(s):  
C R Doering ◽  
J D Gibbon ◽  
D D Holm ◽  
B Nicolaenko
Keyword(s):  
Landau Equation ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Low Dimensional
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