Alexander MIKHAILOV
Applied Math. Department, University of Leeds,
West Yorkshire, Leeds, LS2 9JT, UK
E-mail: sashamik@amsta.leeds.ac.uk
and
L.D. Landau Institute for Theoretical Physics.
Kosygina 2, Moscow, GSP1, RUSSIA

Symmetry approach in differential and symbolic representations

Abstract:
Existence of higher symmetries is the characteristic property of integrable equations. It is a difficult and very delicate problem to describe a variety of equations which possess higher symmetries. The central object of the Symmetry Approach is the concept of formal recursion operator. Symbolic representation, suitable for differential polynomials enables to solve a global problem of classification and give a complete description of equations with symmetries in all orders. Our recent attempt to merge the Symmetry Approach and the Symbolic Method looks promising and suitable for non-evolutionary and multi-dimensional equations.