Abstract
In this paper some travelling wave solutions and conservation laws for the 2D Ricci flow model in conformal gauge are investigated. A guideline able to classify the types of solutions according to the values of some parameters is provided by making use of two versions of the auxiliary equation method. The key feature of these approaches is to take a second order linear ordinary differential equation (ODE), respectively a first order nonlinear ODE with at most an eighth-degree nonlinear term as auxiliary equations. Conserved forms of the travelling wave equation for the Ricci flow are derived through three specific approaches, namely the variational approach, the Ibragimov method for nonlinear self-adjoint differential equations and the one based upon a relationship between conserved forms and their associated symmetries. The former two methods generated similar results, while the latter one has revealed new conserved densities.
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