On the Relation between Lie Symmetries and Prolongation Structures of Nonlinear Field Equations: Non-Local Symmetries

Abstract

An algebraic method is devised to look for non-local symmetries of the pseudopotential type of nonlinear field equations. The method is based on the use of an infinite-dimensional subalgebra of the prolongation algebra associated with the equations under consideration. Our approach, which is applied 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 . The method could be exploited to investigate the symmetry properties of other nonlinear field equations possessing nontrivial prolongations.