Applied Mathematics Seminar

In this talk I shall discuss some of the important open questions in the field of symmetry analysis of differential equations. The ``classical method of symmetry reductions'' is the Lie group method of infinitesimal transformations which dates back to the work of Sophus Lie in the late nineteenth century. During the past decade or so there has been considerable interest in various generalizations of this method, probably due to the increasing availability of symbolic manipulation programs. In particular I shall discuss some of the following topics:

• When does the classical Lie group method need to be generalized?
• Algorithms and symbolic manipulation programs for symmetry analysis.
• Symmetry reductions for differential-difference and difference equations.
• Nonclassical potential symmetries.
• Lie-Bäcklund symmetries and generalizations.
• The nature of ``nonclassical symmetries''
• ``Ansatz'' methods