Applications of Renormgroup Symmetries

Abstract

This chapter is aimed at describing feasible applications of the renormgroup symmetries. In demonstrating the efficiency of this approach we mainly use the algorithm based on approximate groups. The method can be applied to the systems described in terms of models based on differential or integro-differential equations with small parameters. These parameters allows us to consider a simple subsystem of the original equations, treated as the zero-order basic manifold $\mathcal{R}\mathcal{M}$, that usually admits an extended symmetry group inherited by the original equations. Restricting this approximate group on the solution of the boundary value problem yields the desired renormgroup symmetries.