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On the validity of the Ginzburg-Landau equation

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Solutions of the Ginzburg‐Landau Equation of Interest in Shear Flow Transition
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L. Hörmander , Linear Partial Differential Operators. VIII + 284 S. m. 1 Fig. Berlin/Göttingen/Heidelberg 1963. Springer‐Verlag. Preis geb. DM 42,‐ .
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Cellular Structures in Instabilities
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Functions of One Complex Variable
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Linear Partial Differential Operators
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Evolution of Order and Chaos
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Chemical Oscillations, Waves, and Turbulence
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Studies in Non-Linear Stability Theory
inferredcites →https://doi.org/10.1007/978-3-662-02330-3openalex-snapshot
Hydrodynamic Instabilities and the Transition to Turbulence
inferredcites →https://doi.org/10.1007/bf01209150openalex-snapshot
Bifurcating time-periodic solutions of Navier-Stokes equations in infinite cylinders
inferredcites →https://doi.org/10.1007/bf02278004openalex-snapshot
The time dependent amplitude equation for the Swift-Hohenberg problem
inferredcites →https://doi.org/10.1007/bf03167038openalex-snapshot
Primary and secondary bifurcations in the Couette-Taylor problem
inferredcites →https://doi.org/10.1016/0167-2789(86)90114-4openalex-snapshot
Spatial structure of time-periodic solutions of the Ginzburg-Landau equation
inferredcites →https://doi.org/10.1016/0167-2789(86)90140-5openalex-snapshot
Benjamin-Feir turbulence in convective binary fluid mixtures
inferredcites →https://doi.org/10.1016/0167-2789(89)90043-2openalex-snapshot
Strong selection or rejection of spatially periodic patterns in degenerate bifurcations
inferredcites →https://doi.org/10.1016/s0168-2024(08)x7001-8openalex-snapshot
Asymptotic Analysis of Singular Perturbations
inferredcites →https://doi.org/10.1017/s0022112069000127openalex-snapshot
Distant side-walls cause slow amplitude modulation of cellular convection
inferredcites →https://doi.org/10.1017/s0022112069000176openalex-snapshot
Finite bandwidth, finite amplitude convection
inferredcites →https://doi.org/10.1017/s0022112071001733openalex-snapshot
A non-linear instability theory for a wave system in plane Poiseuille flow
inferredcites →https://doi.org/10.1017/s0022112071002337openalex-snapshot
Non-linear wave-number interaction in near-critical two-dimensional flows
inferredcites →https://doi.org/10.1098/rspa.1985.0120openalex-snapshot
Bounded solutions of the nonlinear parabolic amplitude equation for plane Poiseuille flow
inferredcites →https://doi.org/10.1115/1.3167071openalex-snapshot
An Album of Fluid Motion

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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The Validity of Generalized Ginzburg-Landau Equations
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On the Validity of the degenerate Ginzburg—Landau equation
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Modulation equations and parabolic limits of reaction random-walk systems
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Nonlinear Stability of Bifurcating Front Solutions for the Taylor-Couette Problem
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Comparison of Inertial Manifolds and Application to Modulated Systems
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Validity and Limitation of the Newell‐Whitehead Equation
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Phase dynamics in the real Ginzburg‐Landau equation
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Justification of the Ginzburg–Landau approximation for an instability as it appears for Marangoni convection
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Error estimates for the Ginzburg‐Landau approximation: an overview and recent results
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Failure of the N ‐wave interaction approximation without imposing periodic boundary conditions
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Significance of modulated gravity on triple‐diffusive convection of liquids through permeable media: Ginzburg–Landau analysis of heat and mass transfer
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Approximation of the Korteweg–de Vries Equation by the Nonlinear Schrödinger Equation
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Exponential Convergence of the Galerkin Approximation for the Ginzburg-Landau Equation
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Error estimates for the Ginzburg-Landau approximation
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Reduction of PDEs on domains with several unbounded directions: A first step towards modulation equations
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Global existence via Ginzburg-Landau formalism and pseudo-orbits of Ginzburg-Landau approximations
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Diffusive stability of spatial periodic solutions of the Swift-Hohenberg equation
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Traveling waves in the complex Ginzburg-Landau equation
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The Ginzburg-Landau manifold is an attractor
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A new estimate for the Ginzburg-Landau approximation on the real axis
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Singularly Perturbed and Nonlocal Modulation Equations for Systems with Interacting Instability Mechanisms
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Non-linear Stability of Modulated Fronts¶for the Swift-Hohenberg Equation
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Justification of the Ginzburg–Landau Approximation in Case of Marginally Stable Long Waves
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Rise and Fall of Periodic Patterns for a Generalized Klausmeier–Gray–Scott Model
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Derivation of the Time-Dependent Ginzburg-Landau Equation on the Line
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Scaling Methods and Approximative Equations for Homogeneous Reaction—Diffusion Systems and Applications to Epidemics
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The validity of phase diffusion equations and of Cahn–Hilliard equations for the modulation of pattern in reaction–diffusion systems
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Nonlinear convective stability of travelling fronts near Turing and Hopf instabilities
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Attractivity of the Ginzburg–Landau mode distribution for a pattern forming system with marginally stable long modes
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Geometric blow-up of a dynamic Turing instability in the Swift-Hohenberg equation
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The validity of modulation equations for extended systems with cubic nonlinearities
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Justification of mean-field coupled modulation equations
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Existence and stability of standing hole solutions to complex Ginzburg-Landau equations
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Existence and stability of singular heteroclinic orbits for the Ginzburg - Landau equation
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A formal geometric blow-up method for pattern forming systems
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The world of the complex Ginzburg-Landau equation
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A Waiting Time Phenomenon in Pattern Forming Systems
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Les Canards de Turing
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The Long Wave Limit for a Boussinesq Equation
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Complex Ginzburg-Landau equation on networks and its non-uniform dynamics
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RENORMALIZATION AND ASYMPTOTICS
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Justification of the Lugiato-Lefever model from a damped driven $\phi^4$ equation
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Deriving amplitude equations via evolutionary $\Gamma$-convergence
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Spectrum and amplitude equations for scalar delay-differential equations with large delay
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The amplitude system for a Simultaneous short-wave Turing and long-wave Hopf instability
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Large-amplitude modulation of periodic traveling waves
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Rotating spirals in oscillatory media with nonlocal interactions and their normal form
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A linear stability theory on time-invariant and time-dependent spatial domains with symmetry: the drop splash problem
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Formation and Persistence of Spatiotemporal Turing Patterns
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Fractional Dissipative PDEs
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