Asymptotic analysis to domain walls between traveling waves modeled by real coupled Ginzburg-Landau equations

2021 ◽  
Vol 152 ◽  
pp. 111266
Author(s):  
Yue Kai ◽  
Zhixiang Yin
Keyword(s):  
Asymptotic Analysis ◽  
Traveling Waves ◽  
Domain Walls ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations

In–Out Intermittency with Nested Subspaces in a System of Globally Coupled, Complex Ginzburg–Landau Equations

2021 ◽  
Vol 31 (01) ◽  
pp. 2130001
Author(s):  
Gerhard Dangelmayr ◽  
Iuliana Oprea
Keyword(s):  
Normal Form ◽  
Traveling Waves ◽  
Complex Dynamics ◽  
Invariant Subspaces ◽  
Chaotic Attractors ◽  
Governing Equations ◽  
Ginzburg Landau ◽  
Higher Dimensional ◽  
Ginzburg Landau Equations ◽  
Anisotropic Systems

Chaos and intermittency are studied for the system of globally coupled, complex Ginzburg–Landau equations governing the dynamics of extended, two-dimensional anisotropic systems near an oscillatory (Hopf) instability of a basic state with two pairs of counterpropagating, oblique traveling waves. Parameters are chosen such that the underlying normal form, which governs the dynamics of the spatially constant modes, has two symmetry-conjugated chaotic attractors. Two main states residing in nested invariant subspaces are identified, a state referred to as Spatial Intermittency ([Formula: see text]) and a state referred to as Spatial Persistence ([Formula: see text]). The [Formula: see text]-state consists of laminar phases where the dynamics is close to a normal form attractor, without spatial variation, and switching phases with spatiotemporal bursts during which the system switches from one normal form attractor to the conjugated normal form attractor. The [Formula: see text]-state also consists of two symmetry-conjugated states, with complex spatiotemporal dynamics, that reside in higher dimensional invariant subspaces whose intersection forms the 8D space of the spatially constant modes. We characterize the repeated appearance of these states as (generalized) in–out intermittency. The statistics of the lengths of the laminar phases is studied using an appropriate Poincaré map. Since the Ginzburg–Landau system studied in this paper can be derived from the governing equations for electroconvection in nematic liquid crystals, the occurrence of in–out intermittency may be of interest in understanding spatiotemporally complex dynamics in nematic electroconvection.

MODULATIONAL INSTABILITY IN NONLINEAR BI-INDUCTANCE TRANSMISSION LINE

2005 ◽  
Vol 19 (26) ◽  
pp. 3961-3983 ◽  
Author(s):  
E. KENGNE ◽  
KUM K. CLETUS
Keyword(s):  
Plane Wave ◽  
Transmission Line ◽  
Traveling Waves ◽  
Modulational Instability ◽  
Ginzburg Landau ◽  
Complex Demodulation ◽  
Wave Solutions ◽  
Ginzburg Landau Equations ◽  
Nonlinear Plane ◽  
The Right

A nonlinear dissipative transmission line is considered and by performing the complex demodulation technique of the signal which allows, in particularly, to separate the right traveling and left traveling waves, we show that the amplitudes of these waves can be described by a complex coupled Ginzburg–Landau equations (CG-LE). The so-called phase winding solutions of the constructed CG-LE is analyzed. We also study the coherent structures in the obtained complex Ginzburg–Landau system. We show that the constructed CG-LE possesses nonlinear plane wave solutions and the modulational instability of these solutions is analyzed. The condition of the modulational instability is given in term of the coefficients of the constructed CG-LE and then in term of the wavenumber of the two right traveling and left traveling waves in the considered transmission line. The results obtained here show that the nonlinear plane wave solutions of the CG-LE under perturbation with zero wavenumber cannot be stable under modulation.

Asymptotic analysis of the bifurcation diagram for symmetric one-dimensional solutions of the Ginzburg–Landau equations

1999 ◽  
Vol 10 (5) ◽  
pp. 477-495 ◽  
Author(s):  
A. AFTALION ◽  
S. J. CHAPMAN
Keyword(s):  
Asymptotic Analysis ◽  
Bifurcation Diagram ◽  
Triple Point ◽  
Normal Solution ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Landau Parameter ◽  
Formal Asymptotics ◽  
Ginzburg Landau Equations ◽  
The One

The bifurcation of symmetric superconducting solutions from the normal solution is considered for the one-dimensional Ginzburg–Landau equations by the methods of formal asymptotics. The behaviour of the bifurcating branch depends upon the parameters d, the size of the superconducting slab, and κ, the Ginzburg–Landau parameter. It was found numerically by Aftalion & Troy [1] that there are three distinct regions of the (κ, d) plane, labelled S1, S2 and S3, in which there are at most one, two and three symmetric solutions of the Ginzburg–Landau system, respectively. The curve in the (κ, d) plane across which the bifurcation switches from being subcritical to supercritical is identified, which is the boundary between S2 and S1∪S3, and the bifurcation diagram is analysed in its vicinity. The triple point, corresponding to the point at which S1, S2 and S3 meet, is determined, and the bifurcation diagram and the boundaries of S1, S2 and S3 are analysed in its vicinity. The results provide formal evidence for the resolution of some of the conjectures of Aftalion & Troy [1].

scholarly journals Exact Solutions for Domain Walls in Coupled Complex Ginzburg–Landau Equations

2011 ◽  
Vol 80 (6) ◽  
pp. 064001 ◽  
Author(s):  
Tat Leung Yee ◽  
Alan Cheng Hou Tsang ◽  
Boris Malomed ◽  
Kwok Wing Chow
Keyword(s):  
Exact Solutions ◽  
Domain Walls ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations

Asymptotic analysis of a class of Ginzburg–Landau equations in thin multidomains

2016 ◽  
Vol 7 (4) ◽  
Author(s):  
Abdellatif Messaoudi
Keyword(s):  
Asymptotic Analysis ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations

AbstractThis paper addresses the asymptotic analysis of minimizers of the classical Ginzburg–Landau energy in a thin multidomain. More precisely we are interested in the minimization of the energyover all maps

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