The nonlinear analysis of perturbation solution for a parabolic differential system
type: Item
instance of: scholarly article
title: The nonlinear analysis of perturbation solution for a parabolic differential system
zbMATH Open document ID: 1252.35155
DOI: 10.1155/2012/605687
author: Victor F. Dailyudenko
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2012-10-16T00:00:00Z
review text: Summary: By investigation of perturbation solution for nonlinear reaction-diffusion system, we derive related differential model for perturbations that involves weak nonlinearities up to third order. For a first time, this model is shown to result in derivation of the system for amplitude distribution by means of nonlinear integration on orthogonal basis in spatial region. The obtained time-dependent system (TDS) contains all possible functional relations between the modes of wave train under consideration along with delayed relations, and after numerical simulation it provides some conclusions concerning the natural frequency of the investigated self-organization process in active medium. The related matrix and modulo operations which substantiate the derivation of the TDS are also considered.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35A25
zbMATH DE Number: 6093839
zbMATH Keywords: weak nonlinearities up to third order
zbMATH Keywords: self-organization process
Wikidata QID: Q58704887
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/605687
OpenAlex ID: W2114094448
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description: scientific article; zbMATH DE number 6093839