Lie symmetries and related group-invariant solutions of a nonlinear Fokker-Planck equation based on the Sharma-Taneja-Mittal entropy
- Resource Type
- article
- Authors
- Scarfone, A. M.; Wada, T.
- Source
- Brazilian Journal of Physics. August 2009 39(2a)
- Subject
- Nonlinear Fokker-Planck equation
Sharma-Taneja-Mittal entropy
Lie symmetries
Group invariant solutions
- Language
- English
- ISSN
- 0103-9733
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.