ar X iv : h ep - t h / 99 11 12 2 v 1 1 6 N ov 1 99 9 Non - local Symmetries of Nonlinear Field Equations : an Algebraic Approach
نویسندگان
چکیده
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 prolon-gation algebra L associated with the equations under consideration. Our approach, which is applied 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 the non-local symmetries expressed in terms of elements of L. The method could be exploited to investigate the symmetry properties of other nonlinear field equations possessing nontrivial prolongations. 1 Introduction Local symmetries of differential equations (DEs) are defined by infinitesimal operators which generally are functions of the independent and the dependent variables (fields) involved in the equations under consideration. On the contrary, non-local symmetries are characterized by infinitesimal operators depending on the global behavior of the fields, expressed for instance by their integrals [1,2].
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