Preliminary group classification of $(2+1)$-dimensional linear ultraparabolic Kolmogorov–Fokker–Planck equations

Abstract

We make a preliminary group classification of a class of $(2+1)$-dimensional ultraparabolic equations invariant under low-dimensional solvable Lie algebras. It is shown that there exist one, six and four nonequivalent ultraparabolic equations admitting two-, three-, and four-dimensional solvable Lie algebras, respectively.