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The Nonlinear Analysis of Perturbation Solution for a Parabolic Differential System

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  • Victor F. Dailyudenko

Abstract

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.

Suggested Citation

  • Victor F. Dailyudenko, 2012. "The Nonlinear Analysis of Perturbation Solution for a Parabolic Differential System," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-17, September.
    • Handle: RePEc:hin:jijmms:605687
    DOI: 10.1155/2012/605687
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    References listed on IDEAS

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    1. Clerc, Marcel G. & Falcon, Claudio, 2005. "Localized patterns and hole solutions in one-dimensional extended systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(1), pages 48-53.
    2. Dailyudenko, Victor F., 2006. "The integrated and local estimations of instability for a class of autonomous delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 759-768.
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