Applied Math. Department, University of Leeds,
West Yorkshire, Leeds, LS2 9JT, UK
L.D. Landau Institute for Theoretical Physics.
Kosygina 2, Moscow, GSP1, RUSSIA

Symmetry approach in differential and symbolic representations

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.