MG11 
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New solutions of the Ricci flow equation in two dimensions using a linearization approach

Two dimensional Ricci flow equation arises in many areas of physics including lower-dimensional spacetimes models for gravity and cosmology. The linearization approach proves a powerful procedure to generate explicit solutions of the Ricci flow equation. We use a direct non-linear substitution, then split the resulting non-linear equation. This results in a class of special solutions, involving arbitrary functions. Adding supplementary assumptions connected with the symmetries of the concrete physical systems it is possible to get effectively large class of solutions. Some special reductions are also discussed.