Invariant solutions and conservation laws to nonconservative FP equation

YAŞAR E., Özer T.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, cilt.59, sa.9, ss.3203-3210, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 59 Sayı: 9
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1016/j.camwa.2010.03.006
  • Dergi Adı: COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.3203-3210
  • Anahtar Kelimeler: Adjoint equation, Conservation laws, FP equation, Lie symmetries, SYMMETRIES
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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. (C) 2010 Elsevier Ltd. All rights reserved.