Extended symmetry analysis of remarkable (1+2)-dimensional Fokker–Planck equation

We carry out the extended symmetry analysis of an ultraparabolic Fokker-Planck equation with three independent variables, which is also called Kolmogorov and singled within class such equations by its remarkable properties. In particular, essential Lie invariance algebra eight-dimensional, maximum dimension above class. compute complete point pseudogroup using direct method, analyze structure single subgroup. After listing inequivalent one- two-dimensional subalgebras maximal algebras this equation, we exhaustively classify reductions, peculiar generalized reductions relate latter to generating solutions iterative action Lie-symmetry operators. As a result, construct wide families exact in those parameterized arbitrary finite number (1+1)-dimensional linear heat equation. establish similarity (1+2)-dimensional Kramers whose are allows us find these easy way.