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

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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

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Keywords

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

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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