Open AccessSome exact solutions for a unidimensional Fokker-Planck equation by using lie symmetries
Author(s) -
Hugo Hernán Ortíz-Álvarez,
Francy Nelly Jiménez García,
Abel Enrique Posso-Agudelo
Publication year - 2015
Publication title -
revista de matemáticas
Language(s) - English
Resource type - Journals
eISSN - 2215-3373
pISSN - 1409-2433
DOI - 10.15517/rmta.v22i1.17499
Subject(s) - fokker–planck equation , infinitesimal , homogeneous space , lie group , invariant (physics) , symmetry (geometry) , mathematical physics , symmetry group , mathematics , lie theory , lie algebra , diffusion equation , mathematical analysis , physics , classical mechanics , partial differential equation , pure mathematics , adjoint representation of a lie algebra , geometry , lie conformal algebra , economy , economics , service (business)
The Fokker Planck equation appears in the study of diffusion phenomena, stochastics processes and quantum and classical mechanics. A particular case fromthis equation, ut − uxx − xux − u=0, is examined by the Lie group method approach. From the invariant condition it was possible to obtain the infinitesimal generators or vectors associated to this equation, identifying the corresponding symmetry groups. Exact solution were found for each one of this generators and new solution were constructed by using symmetry properties.