Towards classification of -dimensional integrable equations. Integrability conditions I

Abstract

In this paper we attempt to extend the symmetry approach (well developed in the case of (1 + 1)-dimensional equations) to the (2 + 1)-dimensional case. Presence of nonlocal terms in symmetries and conservation laws is the main feature of integrable (2 + 1)-dimensional equations. We have introduced a concept of quasi-local functions to characterize nonlocalities. We have found a few first integrability conditions for a class of scalar equations in terms of quasi-local functions and have demonstrated that they are suitable for testing integrability.