Lie Symmetries of the Nonlinear Fokker-Planck Equation Based on Weighted Kaniadakis Entropy

Iulia-Elena Hirica, Cristina-Liliana Pripoae, Gabriel-Teodor Pripoae and Vasile Preda
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Iulia-Elena Hirica: Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania
Cristina-Liliana Pripoae: Department of Applied Mathematics, The Bucharest University of Economic Studies, Piata Romana 6, RO-010374 Bucharest, Romania
Gabriel-Teodor Pripoae: Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania
Vasile Preda: Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania

Mathematics, 2022, vol. 10, issue 15, 1-22

Abstract: The paper studies the Lie symmetries of the nonlinear Fokker-Planck equation in one dimension, which are associated to the weighted Kaniadakis entropy. In particular, the Lie symmetries of the nonlinear diffusive equation, associated to the weighted Kaniadakis entropy, are found. The MaxEnt problem associated to the weighted Kaniadakis entropy is given a complete solution, together with the thermodynamic relations which extend the known ones from the non-weighted case. Several different, but related, arguments point out a subtle dichotomous behavior of the Kaniadakis constant k , distinguishing between the cases k ∈ ( − 1 , 1 ) and k = ± 1 . By comparison, the Lie symmetries of the NFPEs based on Tsallis q -entropies point out six “exceptional” cases, for: q = 1 2 , q = 3 2 , q = 4 3 , q = 7 3 , q = 2 and q = 3 .

Keywords: nonlinear Fokker-Planck equation; nonlinear diffusive equation; Lie symmetries; weighted entropy; MaxEnt problem; Kaniadakis entropy; Tsallis entropy; STM entropy; Bregman divergence; partial differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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