Abstract

A nonlinear Fokker-Planck equation that arises in the framework of statistical mechanics based on the Sharma-Taneja-Mittal entropy is studied via Lie symmetry analysis. The equation describes kinetic processes in anomalous mediums where both super-diffusive and subdiffusive mechanisms arise contemporarily and competitively. We perform complete group classification of the equation based on two parameters that characterise the underlying Sharma-Taneja-Mittal entropy. For arbitrary values of the parameters, the equation is found to admit a two-dimensional symmetry Lie algebra. We identify and catalogue all the cases in which the equation admits additional Lie point symmetries. We also perform symmetry reductions of the equation and obtain second-order s that describe all essentially different invariant solutions of the equation.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 33
Issue: 5
Year: 2020

DOI: 10.12732/ijam.v33i5.5

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