The renormalization group and the implicit function theorem for amplitude equations

DOI10.1063/1.2956505zbMath1152.81512OpenAlexW2087786366MaRDI QIDQ5505002

Eleftherios Kirkinis

Publication date: 23 January 2009

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.2956505

Mathematics Subject Classification ID

Renormalization group methods in equilibrium statistical mechanics (82B28) Singular perturbations for ordinary differential equations (34E15) Multiple scale methods for ordinary differential equations (34E13) Normal forms for nonlinear problems in mechanics (70K45)

Related Items (6)

A general analytical approximation for nonlinear vibrations analysis of continuous systems using renormalization group method ⋮ Amplitude modulation for the Swift-Hohenberg and Kuramoto-Sivashinski equations ⋮ A Combined Renormalization Group-Multiple Scale Method for Singularly Perturbed Problems ⋮ Examples Illustrating the Use of Renormalization Techniques for Singularly Perturbed Differential Equations ⋮ Variation of Parameters and the Renormalization Group Method ⋮ Approximation of center manifolds on the renormalization group method

Cites Work

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• Deriving amplitude equations for weakly-nonlinear oscillators and their generalizations
• Renormalization group approach to multiscale modelling in materials science
• Simple viscous flows: From boundary layers to the renormalization group
• A Technique for the Numerical Verification of Asymptotic Expansions

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