Group Analysis via Nonclassical Symmetries for Two-Dimensional Ricci Flow Equation

This paper is devoted to obtain the largest possible set of symmetries for the two-dimensional Ricci flow ((2D) Rf) equation. By using the classical symmetry method, the structure of Lie algebra of symmetries is obtained and the optimal system of subalgebras of the equation is constructed. Also some reduced equations and group invariant solutions are obtained. By applying the nonclassical symmetry method for the ((2D) Rf) equation we concluded that the analyzed model do not admit supplementary, nonclassical type, symmetries.