Symmetries and Similarity Reductions of Nonlinear Diffusion Equation**The project supported by the State Key Laboratory of Oil/Gas Reservoir Geology and Exploitation under Grant No. PLN0402 and the Doctor Foundation of Ningbo City under Grant No. 2003A61018

Abstract

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 with the eigenvalue are also obtained with the help of the recursion operator . Using a part of these symmetries we get twelve types of nontrivial new similarity reduction.