Nonlinear Galilei-Invariant PDEs with Infinite-Dimensional Lie Symmetry

A class of nonlinear Galilei-invariant generalizations of the heat equation admitting infinite-dimensional Lie symmetry is presented. Lie symmetries and examples of exact solutions are found for some nonlinear equations generalizing the heat equation. Full sets of the absolute differential invariants for two nonequivalent representations of the Galilei algebra are constructed