Exact solitary wave and periodic-peakon solutions of the complex Ginzburg–Landau equation: Dynamical system approach

2021 ◽  
Author(s):  
Guoan Xu ◽  
Yi Zhang ◽  
Jibin Li
Keyword(s):  
Dynamical System ◽  
Solitary Wave ◽  
System Approach ◽  
Landau Equation ◽  
Ginzburg Landau ◽  
Dynamical System Approach ◽  
Ginzburg Landau Equation

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.

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