Some exact solutions for a unidimensional fokker-planck equation by using lie symmetries

Abstract

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.

Keywords

• grupos de Lie
• ecuaciones diferenciales parciales
• soluciones invariantes
• ecuación de Fokker Planck