Symmetry operators for the Fokker-Plank-Kolmogorov equation with nonlocal quadratic nonlinearity

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6 Citations (Scopus)

Abstract

The Cauchy problem for the Fokker-Plank-Kolmogorov equation with a nonlocal nonlinear drift term is reduced to a similar problem for the correspondent linear equation. The relation between symmetry operators of the linear and nonlinear Fokker-Plank-Kolmogorov equations is considered. Illustrative examples of the one-dimensional symmetry operators are presented.

Original languageEnglish
Article number005
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume3
DOIs
Publication statusPublished - 1 Jan 2007

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Kolmogorov Equation
Nonlinearity
Symmetry
Operator
Linear equation
Cauchy Problem
Term

Keywords

  • Fokker-plank-kolmogorov equation
  • Nonlinear partial differential equations
  • Symmetry operators

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Geometry and Topology

Cite this

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title = "Symmetry operators for the Fokker-Plank-Kolmogorov equation with nonlocal quadratic nonlinearity",
abstract = "The Cauchy problem for the Fokker-Plank-Kolmogorov equation with a nonlocal nonlinear drift term is reduced to a similar problem for the correspondent linear equation. The relation between symmetry operators of the linear and nonlinear Fokker-Plank-Kolmogorov equations is considered. Illustrative examples of the one-dimensional symmetry operators are presented.",
keywords = "Fokker-plank-kolmogorov equation, Nonlinear partial differential equations, Symmetry operators",
author = "Shapovalov, {Aleksandr Vasilievich} and Rezaev, {Roman O.} and Trifonov, {Andrey Yu}",
year = "2007",
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doi = "10.3842/SIGMA.2007.005",
language = "English",
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journal = "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)",
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publisher = "Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine",

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T1 - Symmetry operators for the Fokker-Plank-Kolmogorov equation with nonlocal quadratic nonlinearity

AU - Shapovalov, Aleksandr Vasilievich

AU - Rezaev, Roman O.

AU - Trifonov, Andrey Yu

PY - 2007/1/1

Y1 - 2007/1/1

N2 - The Cauchy problem for the Fokker-Plank-Kolmogorov equation with a nonlocal nonlinear drift term is reduced to a similar problem for the correspondent linear equation. The relation between symmetry operators of the linear and nonlinear Fokker-Plank-Kolmogorov equations is considered. Illustrative examples of the one-dimensional symmetry operators are presented.

AB - The Cauchy problem for the Fokker-Plank-Kolmogorov equation with a nonlocal nonlinear drift term is reduced to a similar problem for the correspondent linear equation. The relation between symmetry operators of the linear and nonlinear Fokker-Plank-Kolmogorov equations is considered. Illustrative examples of the one-dimensional symmetry operators are presented.

KW - Fokker-plank-kolmogorov equation

KW - Nonlinear partial differential equations

KW - Symmetry operators

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