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

The paper studies the Lie symmetries of nonlinear Fokker-Planck equation in one dimension, which are associated to weighted Kaniadakis entropy. In particular, diffusive equation, entropy, found. MaxEnt problem entropy is given a complete solution, together with thermodynamic relations extend known ones from non-weighted case. Several different, but related, arguments point out subtle dichotomous behavior constant k, distinguishing between cases k?(?1,1) and k=±1. By comparison, NFPEs based on Tsallis q-entropies six “exceptional” cases, for: q=12, q=32, q=43, q=73, q=2 q=3.