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

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

1999-11-16

arxiv.org/abs/hep-th/9911122v1

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, no figures

Scientific paper

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 $L$ 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.

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