Reduction of amplitude equations by the renormalization group approach

Kirkinis, E. (2008) Reduction of amplitude equations by the renormalization group approach. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 77(1).

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Abstract

This article elucidates and analyzes the fundamental underlying structure of the renormalization group (RG) approach as it applies to the solution of any differential equation involving multiple scales. The amplitude equation derived through the elimination of secular terms arising from a naive perturbation expansion of the solution to these equations by the RG approach is reduced to an algebraic equation which is expressed in terms of the Thiele semi-invariants or cumulants of the eliminant sequence { Zi } i=1 . Its use is illustrated through the solution of both linear and nonlinear perturbation problems and certain results from the literature are recovered as special cases. The fundamental structure that emerges from the application of the RG approach is not the amplitude equation but the aforementioned algebraic equation. © 2008 The American Physical Society.

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17 citations in Web of Science®

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ID Code: 73429
Item Type: Journal Article
Refereed: Yes
Keywords: Perturbation techniques, Problem solving, Amplitude equations, Renormalization group (RG) approach, Differential equations
DOI: 10.1103/PhysRevE.77.011105
ISSN: 15393755 (ISSN)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Deposited On: 07 Jul 2014 22:47
Last Modified: 09 Jul 2014 06:16

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