Kovalenko S.S.

Symmetry Analysis of a Class of (2+1)-Dimensional Linear Ultra-Parabolic Equations

In this paper, a class of (2+1)-dimensional linear ultra-parabolic equations of the second order is investigated by using the methods of group analysis of differential equations. The class under study generalizes a number of the classical equations of mathematical physics such as the free Kramers equation, the linear Kolmogorov equation etc. The classification of the symmetry properties of equations from the class is carried out by using the well-known Lie–Ovsiannikov algorithm.

Preliminary Group Classification of a Class of Generalized Linear Kolmogorov Equations

The group–theoretic method is a modern research method for studying both linear and nonlinear partial differential equations. By using this method, we construct exact partial classical solutions of equations allowing for non-trivial symmetry groups. In this paper, a class of (2+1)-dimensional generalized linear Kolmogorov equations is considered. Our aim is to investigate symmetry properties of equations from the class and to use them to construct invariant fundamental solutions.