The Nonlinear Analysis of Perturbation Solution for a Parabolic Differential System

The Nonlinear Analysis of Perturbation Solution for a Parabolic Differential System

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 mea...

Full description

Bibliographic Details
Main Author: Victor F. Dailyudenko
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2012/605687
id doaj-416755cc6c084ba086c733497bf9022f
record_format Article
spelling doaj-416755cc6c084ba086c733497bf9022f2020-11-24T21:57:25ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/605687605687The Nonlinear Analysis of Perturbation Solution for a Parabolic Differential SystemVictor F. Dailyudenko0United Institute of Informatics Problems of the National Academy of Sciences of Belarus, Surganov Street 6, 220012, Minsk, BelarusBy 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.http://dx.doi.org/10.1155/2012/605687
collection DOAJ
language English
format Article
sources DOAJ
author Victor F. Dailyudenko
spellingShingle Victor F. Dailyudenko
The Nonlinear Analysis of Perturbation Solution for a Parabolic Differential System
International Journal of Mathematics and Mathematical Sciences
author_facet Victor F. Dailyudenko
author_sort Victor F. Dailyudenko
title The Nonlinear Analysis of Perturbation Solution for a Parabolic Differential System
title_short The Nonlinear Analysis of Perturbation Solution for a Parabolic Differential System
title_full The Nonlinear Analysis of Perturbation Solution for a Parabolic Differential System
title_fullStr The Nonlinear Analysis of Perturbation Solution for a Parabolic Differential System
title_full_unstemmed The Nonlinear Analysis of Perturbation Solution for a Parabolic Differential System
title_sort nonlinear analysis of perturbation solution for a parabolic differential system
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2012-01-01
description 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.
url http://dx.doi.org/10.1155/2012/605687
work_keys_str_mv AT victorfdailyudenko thenonlinearanalysisofperturbationsolutionforaparabolicdifferentialsystem
AT victorfdailyudenko nonlinearanalysisofperturbationsolutionforaparabolicdifferentialsystem
_version_ 1725855752405385216

Similar Items