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

AUTOR(ES)

Scarfone, A. M., Wada, T.

FONTE

Brazilian Journal of Physics

DATA DE PUBLICAÇÃO

2009-08

RESUMO

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.

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