One-Dimensional Fokker–Planck Equation with Quadratically Nonlinear Quasilocal Drift

Research output: Contribution to journalArticle

Abstract

The Fokker–Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian’s iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.

Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalRussian Physics Journal
Volume60
Issue number12
DOIs
Publication statusAccepted/In press - 18 Apr 2018

Fingerprint

Cauchy problem
symmetry
traveling waves
partial differential equations
iteration
scaling
approximation

Keywords

  • Adomian decomposition method
  • exact solutions
  • Lie symmetries
  • nonlinear Fokker–Planck equation
  • quasilocal approximation
  • traveling waves

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

One-Dimensional Fokker–Planck Equation with Quadratically Nonlinear Quasilocal Drift. / Shapovalov, A. V.

In: Russian Physics Journal, Vol. 60, No. 12, 18.04.2018, p. 1-10.

Research output: Contribution to journalArticle

@article{9db901a512664692b77ad8b90f596701,
title = "One-Dimensional Fokker–Planck Equation with Quadratically Nonlinear Quasilocal Drift",
abstract = "The Fokker–Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian’s iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.",
keywords = "Adomian decomposition method, exact solutions, Lie symmetries, nonlinear Fokker–Planck equation, quasilocal approximation, traveling waves",
author = "Shapovalov, {A. V.}",
year = "2018",
month = "4",
day = "18",
doi = "10.1007/s11182-018-1327-4",
language = "English",
volume = "60",
pages = "1--10",
journal = "Russian Physics Journal",
issn = "1064-8887",
publisher = "Consultants Bureau",
number = "12",

}

TY - JOUR

T1 - One-Dimensional Fokker–Planck Equation with Quadratically Nonlinear Quasilocal Drift

AU - Shapovalov, A. V.

PY - 2018/4/18

Y1 - 2018/4/18

N2 - The Fokker–Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian’s iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.

AB - The Fokker–Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian’s iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.

KW - Adomian decomposition method

KW - exact solutions

KW - Lie symmetries

KW - nonlinear Fokker–Planck equation

KW - quasilocal approximation

KW - traveling waves

UR - http://www.scopus.com/inward/record.url?scp=85045419821&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85045419821&partnerID=8YFLogxK

U2 - 10.1007/s11182-018-1327-4

DO - 10.1007/s11182-018-1327-4

M3 - Article

AN - SCOPUS:85045419821

VL - 60

SP - 1

EP - 10

JO - Russian Physics Journal

JF - Russian Physics Journal

SN - 1064-8887

IS - 12

ER -