Asymptotics of the Multidimensional Nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov Equation Near a Quasistationary Solution

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Abstract

Asymptotic solutions of the multidimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation with an influence function that is invariant with respect to a spatial shift are constructed. The asymptotic solutions are perturbations of a spatially-homogeneous quasistationary exact solution. General expressions are illustrated by the example of a two-dimensional equation with a Gaussian initial condition.

Original languageEnglish
JournalRussian Physics Journal
DOIs
Publication statusAccepted/In press - 16 Nov 2015

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perturbation
shift

Keywords

  • asymptotic solutions
  • multidimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation
  • quasistationary solution

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

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title = "Asymptotics of the Multidimensional Nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov Equation Near a Quasistationary Solution",
abstract = "Asymptotic solutions of the multidimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation with an influence function that is invariant with respect to a spatial shift are constructed. The asymptotic solutions are perturbations of a spatially-homogeneous quasistationary exact solution. General expressions are illustrated by the example of a two-dimensional equation with a Gaussian initial condition.",
keywords = "asymptotic solutions, multidimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation, quasistationary solution",
author = "Levchenko, {Evgeniy Anatolievich} and Trifonov, {A. Y.} and Shapovalov, {Aleksandr Vasilievich}",
year = "2015",
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day = "16",
doi = "10.1007/s11182-015-0594-6",
language = "English",
journal = "Russian Physics Journal",
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AU - Levchenko, Evgeniy Anatolievich

AU - Trifonov, A. Y.

AU - Shapovalov, Aleksandr Vasilievich

PY - 2015/11/16

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N2 - Asymptotic solutions of the multidimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation with an influence function that is invariant with respect to a spatial shift are constructed. The asymptotic solutions are perturbations of a spatially-homogeneous quasistationary exact solution. General expressions are illustrated by the example of a two-dimensional equation with a Gaussian initial condition.

AB - Asymptotic solutions of the multidimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation with an influence function that is invariant with respect to a spatial shift are constructed. The asymptotic solutions are perturbations of a spatially-homogeneous quasistationary exact solution. General expressions are illustrated by the example of a two-dimensional equation with a Gaussian initial condition.

KW - asymptotic solutions

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KW - quasistationary solution

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