Invariant solutions and conservation laws to nonconservative FP equation

Emrullah Yaşar, Teoman Özer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

We generate conservation laws for the one dimensional nonconservative Fokker-Planck (FP) equation, also known as the Kolmogorov forward equation, which describes the time evolution of the probability density function of position and velocity of a particle, and associate these, where possible, with Lie symmetry group generators. We determine the conserved vectors by a composite variational principle and then check if the condition for which symmetries associate with the conservation law is satisfied. As the Fokker-Planck equation is evolution type, no recourse to a Lagrangian formulation is made. Moreover, we obtain invariant solutions for the FP equation via potential symmetries.

Original languageEnglish
Pages (from-to)3203-3210
Number of pages8
JournalComputers and Mathematics with Applications
Volume59
Issue number9
DOIs
Publication statusPublished - May 2010

Keywords

  • Adjoint equation
  • Conservation laws
  • FP equation
  • Lie symmetries

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