Power law method for finding soliton solutions of the 2+1 Ricci flow model
The paper reviews few general methods which are usually used for tackling integrable models and for finding their analytic solutions. The Lax formalism and the biliniarization Hirota method will be considered, but the focus will be put on the direct methods which allow solving the equations with soliton type solutions. A general approach for finding such solutions, unifying methods as tanh or G'/G, will be presented. It will be illustrated on the Ricci flow equation in 2+1 dimensions, one of the most fruitful models in studying black holes and in the attempt of obtaining a quantum theory of gravity.