Lie symmetries and related group-invariant solutions of a nonlinear Fokker-Planck equation based on the Sharma-Taneja-Mittal entropy

• Autor(a) principal: Scarfone,A. M.
• Data de Publicação: 2009
• Outros Autores: Wada,T.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Brazilian Journal of Physics
• Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332009000400024
• topic: Nonlinear Fokker-Planck equation; Sharma-Taneja-Mittal entropy; Lie symmetries; Group invariant solutions

In the framework of the statistical mechanics based on the Sharma-Taneja-Mittal entropy we derive a family of nonlinear Fokker-Planck equations characterized by the associated non-increasing Lyapunov functional. This class of equations describes kinetic processes in anomalous mediums where both super-diffusive and subdiffusive mechanisms arise contemporarily and competitively. We classify the Lie symmetries and derive the corresponding group-invariant solutions for the physically meaningful Uhlenbeck-Ornstein process. For the purely diffusive process we show that any localized state asymptotically approaches a bell shape well fitted by a generalized Gaussian which is, in general, a quasi-self-similar solution for this class of purely diffusive equations.