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Renormalization Group and the Ginzburg-Landau equation

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What this work says

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

inferredcites →https://doi.org/10.1002/cpa.3160470606openalex-snapshot
Renormalization group and asymptotics of solutions of nonlinear parabolic equations
inferredcites →https://doi.org/10.1007/bf02099141openalex-snapshot
Solutions without phase-slip for the Ginsburg-Landau equation
inferredcites →https://doi.org/10.1016/0001-8708(78)90130-5openalex-snapshot
Multidimensional nonlinear diffusion arising in population genetics
inferredcites →https://doi.org/10.1016/0167-2789(85)90094-6openalex-snapshot
Pattern propagation in nonlinear dissipative systems
inferredcites →https://doi.org/10.1016/s0167-2789(85)80001-4openalex-snapshot
Dynamical properties of propagating front solutions of the amplitude equation
inferredcites →https://doi.org/10.1088/0951-7715/5/6/004openalex-snapshot
Space-time behaviour in problems of hydrodynamic type: a case study
inferredcites →https://doi.org/10.1090/memo/0285openalex-snapshot
Convergence of solutions of the Kolmogorov equation to travelling waves
inferredcites →https://doi.org/10.1103/physrevlett.64.1361openalex-snapshot
Anomalous dimensions and the renormalization group in a nonlinear diffusion process

What points at this work

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

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Diffusive Stability and Self-Similar Decay for the Harmonic Map Heat Flow
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Nonlinear Stability of Bifurcating Front Solutions for the Taylor-Couette Problem
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Renormalization group and asymptotics of solutions of nonlinear parabolic equations
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Phase dynamics in the real Ginzburg‐Landau equation
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Diffusive stability for periodic metric graphs
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Renormalization-Group Method for Reduction of Evolution Equations; Invariant Manifolds and Envelopes
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Renormalization Group Method Applied to Kinetic Equations: Roles of Initial Values and Time
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Renormalizing partial differential equations
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Renormalization Group for Fronts and Patterns
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The Turing Instability in Case of an Additional Conservation Law—Dynamics Near the Eckhaus Boundary and Open Questions
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Critical Phenomena on Large Graphs with Regular Subgraphs
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When Feedbacks Matter: Epidemics, Synchronization, and Self-regulation in Complex Networks
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Stability and Diffusive Dynamics on Extended Domains
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Nonlinear Dynamics of Extended Systems
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Non Linear Parabolic Evolutions in Unbounded Domains
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Diffusion in Random and Non-Linear PDE’s
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Renormalization Group and Nonlinear PDE’s
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The non-linear stability of front solutions for parabolic partial differential equations
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Stability of moving fronts in the Ginzburg-Landau equation
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Diffusive stability of spatial periodic solutions of the Swift-Hohenberg equation
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Bifurcating fronts for the Taylor—Couette problem in infinite cylinders
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Exchange of stability and finite-dimensional dynamics in a bifurcation problem with marginally stable continuous spectrum
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A waiting time phenomenon for modulations of pattern in reaction–diffusion systems
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Asymptotic stability of the critical Fisher–KPP front using pointwise estimates
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Self-Similar Decay of Spatially Localized Perturbations of the Nusselt Solution for the Inclined Film Problem
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Nonlinear Stability and Asymptotic Behavior of Periodic Wave Trains in Reaction–Diffusion Systems Against $$C_{\textrm{ub}}$$-perturbations
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Asymptotic Behavior Near Transition Fronts for Equations of Generalized Cahn–Hilliard Form
inferred← citeshttps://doi.org/10.1007/s00220-022-04619-zopenalex-snapshot
Nonlinear Stability of Periodic Roll Solutions in the Real Ginzburg–Landau Equation Against $$C_{\textrm{ub}}^m$$-Perturbations
inferred← citeshttps://doi.org/10.1007/s002200050495openalex-snapshot
Diffusive Mixing of Stable States in the Ginzburg-Landau Equation
inferred← citeshttps://doi.org/10.1007/s002200100577openalex-snapshot
Non-linear Stability of Modulated Fronts¶for the Swift-Hohenberg Equation
inferred← citeshttps://doi.org/10.1007/s10884-013-9335-0openalex-snapshot
Diffusive Stability of Turing Patterns via Normal Forms
inferred← citeshttps://doi.org/10.1007/s10955-007-9313-1openalex-snapshot
Nonlinear Diffusion Through Large Complex Networks Containing Regular Subgraphs
inferred← citeshttps://doi.org/10.1007/s11071-016-3298-8openalex-snapshot
The renormalization method based on the Taylor expansion and applications for asymptotic analysis
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Stable nongaussian diffusive profiles
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Lie-point symmetries of discrete versus continuous dynamical systems
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Selection, stability and renormalization
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Random walks and flights over connected graphs and complex networks
inferred← citeshttps://doi.org/10.1016/j.cnsns.2025.109548openalex-snapshot
Renormalization group based implicit function approach to connecting orbits
inferred← citeshttps://doi.org/10.1016/j.jde.2004.07.029openalex-snapshot
Self-similar decay of localized perturbations in the integral boundary layer equation
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The validity of phase diffusion equations and of Cahn–Hilliard equations for the modulation of pattern in reaction–diffusion systems
inferred← citeshttps://doi.org/10.1016/j.jde.2011.10.014openalex-snapshot
Diffusive mixing of periodic wave trains in reaction–diffusion systems
inferred← citeshttps://doi.org/10.1016/j.jde.2019.09.056openalex-snapshot
Global existence and decay in nonlinearly coupled reaction-diffusion-advection equations with different velocities
inferred← citeshttps://doi.org/10.1016/j.jde.2020.05.012openalex-snapshot
Asymptotic stability of the critical pulled front in a Lotka-Volterra competition model
inferred← citeshttps://doi.org/10.1016/j.jde.2024.03.017openalex-snapshot
Diffusive stability and self-similar decay for the harmonic map heat flow
inferred← citeshttps://doi.org/10.1016/j.physd.2007.03.018openalex-snapshot
Asymptotic behavior near planar transition fronts for the Cahn–Hilliard equation
inferred← citeshttps://doi.org/10.1016/j.physrep.2003.08.001openalex-snapshot
Front propagation into unstable states
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Almost global existence and transient self similar decay for Poiseuille flow at criticality for exponentially long times
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Renormalization group derivation of phase equations
inferred← citeshttps://doi.org/10.1016/s0378-4371(99)00397-0openalex-snapshot
Renormalization group analysis of differential equations subject to slowly modulated perturbations
inferred← citeshttps://doi.org/10.1016/s1874-575x(02)80036-4openalex-snapshot
The Ginzburg-Landau Equation in Its Role as a Modulation Equation
inferred← citeshttps://doi.org/10.1016/s1874-575x(02)80039-xopenalex-snapshot
Stability of Travelling Waves
inferred← citeshttps://doi.org/10.1017/cbo9780511814921.008openalex-snapshot
Scaling and transformation groups. Renormalization group
inferred← citeshttps://doi.org/10.1017/cbo9781107050242openalex-snapshot
Scaling, Self-similarity, and Intermediate Asymptotics
inferred← citeshttps://doi.org/10.1017/cbo9781107050242.001openalex-snapshot
Preface
inferred← citeshttps://doi.org/10.1017/cbo9781107050242.002openalex-snapshot
Foreword
inferred← citeshttps://doi.org/10.1017/cbo9781107050242.003openalex-snapshot
Introduction
inferred← citeshttps://doi.org/10.1017/cbo9781107050242.004openalex-snapshot
Dimensions, dimensional analysis and similarity
inferred← citeshttps://doi.org/10.1017/cbo9781107050242.005openalex-snapshot
The construction of intermediate-asymptotic solutions using dimensional analysis. Self-similar solutions
inferred← citeshttps://doi.org/10.1017/cbo9781107050242.006openalex-snapshot
Self-similarities of the second kind: first examples
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Self-similarities of the second kind: further examples
inferred← citeshttps://doi.org/10.1017/cbo9781107050242.008openalex-snapshot
Classification of similarity rules and self-similar solutions. A recipe for the application of similarity analysis
inferred← citeshttps://doi.org/10.1017/cbo9781107050242.009openalex-snapshot
Scaling and transformation groups. Renormalization group
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Self-similar solutions and travelling waves
inferred← citeshttps://doi.org/10.1017/cbo9781107050242.011openalex-snapshot
Invariant solutions: asymptotic conservation laws, spectrum of eigenvalues, and stability
inferred← citeshttps://doi.org/10.1017/cbo9781107050242.012openalex-snapshot
Scaling in the deformation and fracture of solids
inferred← citeshttps://doi.org/10.1017/cbo9781107050242.013openalex-snapshot
Scaling in turbulence
inferred← citeshttps://doi.org/10.1017/cbo9781107050242.014openalex-snapshot
Scaling in geophysical fluid dynamics
inferred← citeshttps://doi.org/10.1017/cbo9781107050242.015openalex-snapshot
Scaling: miscellaneous special problems
inferred← citeshttps://doi.org/10.1017/cbo9781107050242.016openalex-snapshot
Afterword
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References
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