Compatibility and generalised conditional symmetries

It is shown that the determining equations for generalised conditional symmetries (GCSs) of order n, of an evolution equation of arbitrary order, can be found as a consequence of compatibility with an nth-order invariant surface condition. The compatibility technique is demonstrated on a second-order nonlinear diffusion-convection equation with absorption and used to find new GCSs of a linear diffusion equation with nonlinear source. (c) 2006 Elsevier B.V. All rights reserved.