Symmetries and similarity reductions of Nonlinear diffusion equation

The inverse recursion operator, three new sets of symmetries, and infinite-dimensional Lie algebras for the nonlinear diffusion equation are given. Some nonlocal symmetries related to eigenvectors of the recursion operator 4) with the eigenvalue lambda(i) are also obtained with the help of the recursion operator Phi(i) = Phi - lambda(i). Using a part of these symmetries we get twelve types of nontrivial new similarity reduction.