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

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    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

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    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

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    title = "Approximate Solutions of the One-Dimensional Fisher–Kolmogorov–Petrovskii– Piskunov Equation with Quasilocal Competitive Losses",
    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.",
    keywords = "Fisher–Kolmogorov–Petrovskii–Piskunov equation, perturbation method, quasilocal competitive losses, separation of variables",
    author = "Shapovalov, {A. V.}",
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    AB - 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.

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    KW - separation of variables

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