The world of the complex Ginzburg-Landau equation (Q3077101)

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scientific article

Language	Label	Description	Also known as
English	The world of the complex Ginzburg-Landau equation	scientific article

Statements

scholarly article

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The world of the complex Ginzburg-Landau equation (English)

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Igor S. Aranson

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Reviews of Modern Physics

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publication date

21 February 2011

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full work available at URL

https://arxiv.org/abs/cond-mat/0106115

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MaRDI profile type

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On the interaction of spiral waves in non-equilibrium media

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Stability of periodic waves governed by the modified Kawahara equation

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Synchronized disorder in a 2D complex Ginzburg-Landau equation

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The topological space of all extreme points of a compact convex set

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Structure and dynamics of dislocations in anisotropic pattern-forming systems

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The structure of spiral-domain patterns and shocks in the \(2\)D complex Ginzburg-Landau equation

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Absolute and convective instabilities of spatially periodic flows

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Long-range order with local chaos in lattices of diffusively coupled ODEs

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Modulated amplitude waves and defect formation in the one-dimensional complex Ginzburg-Landau equation

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Spatiotemporal intermittency regimes of the one-dimensional complex Ginzburg-Landau equation

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Forcing oscillatory media: phase kinks vs. synchronization.

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Strong resonances of spatially distributed oscillators: A laboratory to study patterns and defects

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EXCITABLE SPIRAL WAVES IN NEMATIC LIQUID CRYSTALS

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Pattern formation outside of equilibrium

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Non-linear wave-number interaction in near-critical two-dimensional flows

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Breaking the hidden symmetry in the Ginzburg-Landau equation

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Low-dimensional behaviour in the complex Ginzburg-Landau equation

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Dynamics of phase singularities in two-dimensional oscillating systems

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Hydromagnetic convection in a rapidly rotating fluid layer

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Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation

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Dynamics of spiral rings in the three dimensional Ginzburg-Landau equation

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Viscoelastic behaviour of cellular solutions to the Kuramoto-Sivashinsky model

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The dynamics of scroll wave filaments in the complex Ginzburg-Landau equation

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Target patterns in reaction-diffusion systems

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Spiral Waves in Reaction-Diffusion Equations

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On the nonlinear response of a marginally unstable plane parallel flow to a two-dimensional disturbance

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A nonlinear instability burst in plane parallel flow

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Composite ``zigzag'' structures in the 1D complex Ginzburg-Landau equation

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The Eckhaus instability for traveling waves

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Existence and stability of standing hole solutions to complex Ginzburg-Landau equations

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Helical and circular scroll wave filaments

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The dynamics of helical scroll waves in excitable media

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Topology of cosmic domains and strings

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Characterization of dispersive chaos and related states of binary-fluid convection

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On the Eckhaus instability for spatially periodic patterns

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Traveling hole solutions of the complex Ginzburg-Landau equation: A review

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Traveling hole solutions to the complex Ginzburg-Landau equation as perturbations of nonlinear Schrödinger dark solitons

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Universal description of laser dynamics near threshold

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Inertial ranges for turbulent solutions of complex Ginzburg-Landau equations.

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Convection in binary mixtures: The role of the concentration field

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Finite amplitude cellular convection

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Phase turbulence in the two-dimensional complex Ginzburg-Landau equation

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Derivation of the time-dependent Ginzburg-Landau equation on the line

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Bounds for the solutions of the complex Ginzburg-Landau equation in terms of the dispersion parameters

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Spirals in liquid crystals in a rotating magnetic field

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Order parameter equations for long-wavelength instabilities

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Vortices in complex scalar fields

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Vortex dynamics of the nonlinear wave equation

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Finite bandwidth, finite amplitude convection

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Numerical study of hydrodynamics using the nonlinear Schrödinger equation

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Towards a universal theory for natural patterns

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Structure and dynamics of defects in 2D complex vector field

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On interaction of spiral waves

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Stability of vortex rings in a model of superflow

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Motion of vortex lines in the Ginzburg-Landau model

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The cubic complex Ginzburg-Landau equation for a backward bifurcation

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Localized states in fluid convection and multi-photon lasers

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Interaction of defects in two-dimensional systems

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Analytical description of a state dominated by spiral defects in two-dimensional extended systems

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Dynamics of defects in the complex Ginzburg-Landau equation

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The contributions of Da Rios and Levi-Civita to asymptotic potential theory and vortex filament dynamics

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The stability of standing waves with small group velocity

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A bound on the decay of defect-defect correlation functions in two-dimensional complex order parameter equations

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Vortex motion in the spatially inhomogeneous conservative Ginzburg-Landau model

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Global existence via Ginzburg-Landau formalism and pseudo-orbits of Ginzburg-Landau approximations

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Distant side-walls cause slow amplitude modulation of cellular convection

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Spatiotemporal chaos in the one-dimensional complex Ginzburg-Landau equation

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MULTI-ARMED SPIRALS IN A LIGHT-CONTROLLED EXCITABLE REACTION

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A non-linear instability theory for a wave system in plane Poiseuille flow

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On the non-linear mechanics of wave disturbances in stable and unstable parallel flows Part 1. The basic behaviour in plane Poiseuille flow

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Nonlinear Stability Theory

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On the mathematics of Taylor-vortex flows in cylinders of finite length

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All we know about hole solutions in the CGLE

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Convective and absolute instabilities of fluid flows in finite geometry

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Bifurcation analysis of the Eckhaus instability

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Singular perturbation theory of traveling waves in excitable media (A review)

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On the validity of the Ginzburg-Landau equation

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Sources, sinks and wavenumber selection in coupled CGL equations and experimental implications for counter-propagating wave systems

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Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations

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Stability limits of traveling waves and the transition to spatiotemporal chaos in the complex Ginzburg-Landau equation

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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cond-mat/0106115

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10.1103/REVMODPHYS.74.99

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Sitelinks

Mathematics(1 entry)

mardi Publication:3077101

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