Analytic linearization of PDE´s through Lie symmetries

In recent years, some new results have been established about the linearization of finite-dimensional nonlinear dynamical systems by means of diffeomorphisms, being analytic at the origin. Such results are based on the knowledge of a particular Lie-symmetry of the given system about the origin. In this paper, a class of nonlinear PDE´s is considered, for which a similar necessary and sufficient condition for linearization about the “origin” is derived. As in the case of finite-dimensional linear systems, the knowledge of a Lie symmetry allows the use of known techniques for the computation of the (exact or approximated) linearizing change of coordinates.