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Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433

Rev. Mat vol.22 n.1 San José Jan./Jun. 2015


Some exact solutions for a unidimensional fokker-planck equation by using Lie Symmetries

Algunas soluciones exactas para la ecuación unidimensional de fokker-planck usando Simetrías de Lie

Hugo Hernán Ortiz-Álvarez*+, Francy Nelly Jiménez-García*, Abel Enrique Posso-Agudelo*


The Fokker Planck equation appears in the study of diffusion phenomena, stochastics processes and quantum and classical mechanics. A particular case from this equation, ut — uxx — xux — u = 0, is examined by the Lie group method approach. From the invari-ant 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: Lie groups; partial differential equations; invariant solutions; Fokker Planck equation.


La ecuación de Fokker Planck aparece en el estudio de fenómenos de difusión, procesos estocásticos y mecánica clasica y cuántica. Un caso particular de esta ecuacion, ut — uxx — xux — u = 0, es analizada empleando el método de los grupos de Lie. De la condición de invariación fue posible obtener los generadores infinitesimales o vectores de la ecuación identificando los correspondientes grupos de simetría. Se obtuvieron soluciones exactas para cada uno de estos generadores y se construyeron nuevas soluciones aplicando propiedades de simetría.

Palabras clave: grupos de Lie; ecuaciones diferenciales parciales; soluciones invariantes; ecuación de Fokker Planck.

Mathematics Subject Classification: 35A30.

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*Universidad de Caldas & Universidad Nacional de Colombia, Manizales, Colombia. E-Mail:
Universidad Autónoma & Universidad Nacional de Colombia, Manizales, Colombia. E-Mail:
Universidad Tecnológica, Pereira, Colombia. E-Mail:

Received: 5/May/2013; Revised: 28/Aug/2014; Accepted: 17/Oct/2014.

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