On the relation between Lie symmetries and prolongation structures of nonlinear field equations - Non-local symmetries

An algebraic method is devised to look for non-local symmetries of the pseu dopotential type of nonlinear field equations. The method is based on the u se of an infinite-dimensional subalgebra of the prolongation algebra L asso ciated with the equations under consideration. Our approach, which is appli ed by way of example to the Dym and the Korteweg-de Vries equation, allows us to obtain a general formula for the infinitesimal operator of non-local symmetries expressed in terms of elements of L. The method could be exploit ed to investigate the symmetry properties of other nonlinear field equation s possessing nontrivial prolongations.