Coherent and incoherent structures in systems described by the 1D CGLE: experiments and identification

DOI10.1016/S0167-2789(02)00687-5zbMath1076.76525arXivcond-mat/0110068OpenAlexW2592381737MaRDI QIDQ1851377

Martin van Hecke

Publication date: 16 December 2002

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/cond-mat/0110068

zbMATH Keywords

local twist structures

Mathematics Subject Classification ID

Nonlinear effects in hydrodynamic stability (76E30) Experimental work for problems pertaining to fluid mechanics (76-05)

Related Items (14)

Instability of periodic traveling wave solutions in a modified Fitzhugh-Nagumo model for excitable media ⋮ Birth-death process of local structures in defect turbulence described by the one-dimensional complex Ginzburg-Landau equation ⋮ Dynamic behavior and stability analysis of nonlinear modes in the fourth-order generalized Ginzburg-Landau model with near \(\mathcal{PT}\)-symmetric potentials ⋮ Stability of periodic traveling waves in the Aliev-Panfilov reaction-diffusion system ⋮ Numerical continuation methods for studying periodic travelling wave (wavetrain) solutions of partial differential equations ⋮ Numerical continuation of invariant solutions of the complex Ginzburg-Landau equation ⋮ Wave train selection behind invasion fronts in reaction-diffusion predator-prey models ⋮ Dark soliton dynamics under the complex Ginzburg-Landau equation ⋮ Locating the transition from periodic oscillations to spatiotemporal chaos in the wake of invasion ⋮ Spiral patterns and numerical bifurcation analysis in a three-component Brusselator model for chemical reactions ⋮ Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II: Convective/absolute transitions ⋮ Sources and sinks in 1D traveling waves ⋮ Nonlinear analysis of the Eckhaus instability: Modulated amplitude waves and phase chaos with nonzero average phase gradient ⋮ Inhibitor-induced wavetrains and spiral waves in an extended FitzHugh-Nagumo model of nerve cell dynamics

Cites Work

• Critical properties of convective waves in a one-dimensional system
• All we know about hole solutions in the CGLE
• On the Eckhaus instability for spatially periodic patterns
• The Eckhaus instability for traveling waves
• Spatiotemporal chaos in the one-dimensional complex Ginzburg-Landau equation
• Erratum: Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations
• On the analysis of spatiotemporally chaotic data
• The stability of standing waves with small group velocity
• The world of the complex Ginzburg-Landau equation
• Spatiotemporal intermittency regimes of the one-dimensional complex Ginzburg-Landau equation
• Pattern formation outside of equilibrium
• The disintegration of wave trains on deep water Part 1. Theory
• Composite ``zigzag structures in the 1D complex Ginzburg-Landau equation
• Modulated amplitude waves and defect formation in the one-dimensional complex Ginzburg-Landau equation

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