Non-local Symmetries of Nonlinear Field Equations: an Algebraic Approach

摘要

An algebraic method is devised to look for non-local symmetries of thepseudopotential type of nonlinear field equations. The method is based on theuse of an infinite-dimensional subalgebra of the prolongation algebra $L$associated with the equations under consideration. Our approach, which isapplied by way of example to the Dym and the Korteweg-de Vries equations,allows us to obtain a general formula for the infinitesimal operator of thenon-local symmetries expressed in terms of elements of $L$. The method could beexploited to investigate the symmetry properties of other nonlinear fieldequations possessing nontrivial prolongations.