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2D general nonlinear parabolic equation for unstable wave package envelope in structural macrokinetics

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Abstract

We reduce the mathematical model for a chemical reaction in a moving medium to the general nonlinear parabolic equation (GNPE) for the complex amplitude of envelope wave to analyse weakly nonlinear interactions in supercritical regions. We use the method of many scales, wave packages, modification of Mandelshtam method and take into account the group velocity of envelope wave that is typical for nonlinear dispersive medium. GNPE describes the long-term system behaviour after stability loss and its coefficients are explicitly expressed through parameters of the initial nonlinear partial differential equations. It is taking into account the location of wave packet centre out of harmonics with maximum increment.

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Authors and Affiliations

  1. South Ural State University, 76, Lenin ave, Chelyabinsk, Russia, 454080

    Inna Elyukhina

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  1. Inna Elyukhina
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Correspondence to Inna Elyukhina.

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Elyukhina, I. 2D general nonlinear parabolic equation for unstable wave package envelope in structural macrokinetics. J Math Chem 56, 2617–2625 (2018). https://doi.org/10.1007/s10910-018-0907-4

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  • DOI: https://doi.org/10.1007/s10910-018-0907-4

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