Symmetries of the Fisher-Kolmogorov-Petrovskii-Piskunov equation with a nonlocal nonlinearity in a semiclassical approximation

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7 Citations (Scopus)

Abstract

The classical group analysis approach used to study the symmetries of integro-differential equations in a semiclassical approximation is considered for a class of nearly linear integro-differential equations. In a semiclassical approximation, an original integro-differential equation leads to a finite consistent system of differential equations whose symmetries can be calculated by performing standard group analysis.The approach is illustrated by the calculation of the Lie symmetries in explicit form for a special case of the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov population equation.

Original languageEnglish
Pages (from-to)716-726
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume395
Issue number2
DOIs
Publication statusPublished - 15 Nov 2012

Fingerprint

Semiclassical Approximation
Integrodifferential equations
Integro-differential Equation
Nonlinearity
Symmetry
Lie Symmetry
Classical Groups
System of Differential Equations
Linear equation
Differential equations

Keywords

  • Fisher-Kolmogorov-Petrovskii-Piskunov equation
  • Integro-differential equation
  • Lie symmetries
  • Nearly linear equation
  • Semiclassical approximation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

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title = "Symmetries of the Fisher-Kolmogorov-Petrovskii-Piskunov equation with a nonlocal nonlinearity in a semiclassical approximation",
abstract = "The classical group analysis approach used to study the symmetries of integro-differential equations in a semiclassical approximation is considered for a class of nearly linear integro-differential equations. In a semiclassical approximation, an original integro-differential equation leads to a finite consistent system of differential equations whose symmetries can be calculated by performing standard group analysis.The approach is illustrated by the calculation of the Lie symmetries in explicit form for a special case of the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov population equation.",
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AU - Levchenko, Evgeniy Anatolievich

AU - Shapovalov, Aleksandr Vasilievich

AU - Trifonov, A. Yu

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AB - The classical group analysis approach used to study the symmetries of integro-differential equations in a semiclassical approximation is considered for a class of nearly linear integro-differential equations. In a semiclassical approximation, an original integro-differential equation leads to a finite consistent system of differential equations whose symmetries can be calculated by performing standard group analysis.The approach is illustrated by the calculation of the Lie symmetries in explicit form for a special case of the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov population equation.

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