Invariant solutions and conservation laws to nonconservative FP equation


YAŞAR E., Özer T.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol.59, no.9, pp.3203-3210, 2010 (SCI-Expanded) identifier identifier

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