The renormalization group and the implicit function theorem for amplitude equations

Kirkinis, E. (2008) The renormalization group and the implicit function theorem for amplitude equations. Journal of Mathematical Physics, 49(7).

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Abstract

This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen, Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation for both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases. © 2008 American Institute of Physics.

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ID Code: 73430
Item Type: Journal Article
Refereed: Yes
DOI: 10.1063/1.2956505
ISSN: 00222488 (ISSN)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Deposited On: 07 Jul 2014 22:45
Last Modified: 09 Jul 2014 06:23

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