International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 605687, 17 pages
Research Article

The Nonlinear Analysis of Perturbation Solution for a Parabolic Differential System

United Institute of Informatics Problems of the National Academy of Sciences of Belarus, Surganov Street 6, 220012, Minsk, Belarus

Received 9 April 2012; Revised 19 June 2012; Accepted 30 July 2012

Academic Editor: Yuri Latushkin

Copyright © 2012 Victor F. Dailyudenko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.