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Lie symmetries of fundamental solutions of one (2+1)-dimensional ultra-parabolic Fokker--Planck--Kolmogorov equation (1408.0166v1)
Published 1 Aug 2014 in math-ph, math.AP, and math.MP
Abstract: A (2+1)-dimensional linear ultra-parabolic Fokker--Planck--Kolmogorov equation is investigated from the group-theoretical point of view. By using the Berest--Aksenov approach, an algebra of invariance of fundamental solutions of the equation is found. A fundamental solution of the equation under study is computed in an explicit form as a weak invariant solution.