Symmetries of the One-Dimensional Fokker–Planck–Kolmogorov Equation with a Nonlocal Quadratic Nonlinearity

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Abstract

The one-dimensional Fokker–Planck–Kolmogorov equation with a special type of nonlocal quadratic nonlinearity is represented as a consistent system of differential equations, including a dynamical system describing the evolution of the moments of the unknown function. Lie symmetries are found for the consistent system using methods of classical group analysis. An example of an invariant-group solution obtained with an additional integral constraint imposed on the system is considered.

Original languageEnglish
Pages (from-to)1-8
Number of pages8
JournalRussian Physics Journal
Volume60
Issue number2
DOIs
Publication statusAccepted/In press - 31 May 2017

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nonlinearity
symmetry
dynamical systems
differential equations
moments

Keywords

  • consistent system
  • invariant-group solution
  • Lie symmetries
  • nonlinear Fokker–Planck–Kolmogorov equation

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

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abstract = "The one-dimensional Fokker–Planck–Kolmogorov equation with a special type of nonlocal quadratic nonlinearity is represented as a consistent system of differential equations, including a dynamical system describing the evolution of the moments of the unknown function. Lie symmetries are found for the consistent system using methods of classical group analysis. An example of an invariant-group solution obtained with an additional integral constraint imposed on the system is considered.",
keywords = "consistent system, invariant-group solution, Lie symmetries, nonlinear Fokker–Planck–Kolmogorov equation",
author = "Levchenko, {E. A.} and Trifonov, {A. Y.} and Shapovalov, {A. V.}",
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AU - Trifonov, A. Y.

AU - Shapovalov, A. V.

PY - 2017/5/31

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AB - The one-dimensional Fokker–Planck–Kolmogorov equation with a special type of nonlocal quadratic nonlinearity is represented as a consistent system of differential equations, including a dynamical system describing the evolution of the moments of the unknown function. Lie symmetries are found for the consistent system using methods of classical group analysis. An example of an invariant-group solution obtained with an additional integral constraint imposed on the system is considered.

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KW - Lie symmetries

KW - nonlinear Fokker–Planck–Kolmogorov equation

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