Approximate Solutions of the One-Dimensional Fisher–Kolmogorov–Petrovskii– Piskunov Equation with Quasilocal Competitive Losses

A. V. Shapovalov

    Research output: Contribution to journal › Article

    Abstract

    The modified Fisher–Kolmogorov–Petrovskii–Piskunov equation with quasilocal quadratic competitive losses and variable coefficients in the small nonlocality parameter approximation is reduced to an equation with a nonlinear diffusion coefficient. Within the framework of a perturbation method, equations are obtained for the first terms of an asymptotic expansion of an approximate solution of the reduced equation. Particular solutions in separating variables are considered for the equations determining the first terms of the asymptotic series. The problem is reduced to an elliptic integral and one linear, homogeneous ordinary differential equation.

    LanguageEnglish
    Pages1461-1468
    Number of pages8
    JournalRussian Physics Journal
    Volume60
    Issue number9
    DOIs
    Publication statusPublished - 1 Jan 2018

    Fingerprint

    asymptotic series
    elliptic functions
    differential equations
    diffusion coefficient
    perturbation
    expansion
    coefficients
    approximation

    Keywords

    • Fisher–Kolmogorov–Petrovskii–Piskunov equation
    • perturbation method
    • quasilocal competitive losses
    • separation of variables

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    Approximate Solutions of the One-Dimensional Fisher–Kolmogorov–Petrovskii– Piskunov Equation with Quasilocal Competitive Losses. / Shapovalov, A. V.

    In: Russian Physics Journal, Vol. 60, No. 9, 01.01.2018, p. 1461-1468.

    Research output: Contribution to journal › Article

    Shapovalov, AV 2018, 'Approximate Solutions of the One-Dimensional Fisher–Kolmogorov–Petrovskii– Piskunov Equation with Quasilocal Competitive Losses' Russian Physics Journal, vol. 60, no. 9, pp. 1461-1468. https://doi.org/10.1007/s11182-018-1236-6
    Shapovalov AV. Approximate Solutions of the One-Dimensional Fisher–Kolmogorov–Petrovskii– Piskunov Equation with Quasilocal Competitive Losses. Russian Physics Journal. 2018 Jan 1;60(9):1461-1468. https://doi.org/10.1007/s11182-018-1236-6
    Shapovalov, A. V. / Approximate Solutions of the One-Dimensional Fisher–Kolmogorov–Petrovskii– Piskunov Equation with Quasilocal Competitive Losses. In: Russian Physics Journal. 2018 ; Vol. 60, No. 9. pp. 1461-1468.
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