
Journal of Lie Theory 20 (2010), No. 2, 375392 Copyright Heldermann Verlag 2010 On a Lie Group Characterization of QuasiLocal Symmetries of Nonlinear Evolution Equations Renat Zhdanov BIOkey International, Eagan, MN 55123, U.S.A. renat.zhdanov@biokey.com We develop an efficient algebraic approach to classifying nonlinear evolution equations in one spatial dimension that admit nonlocal transformation groups (quasilocal symmetries), i.e., groups involving integrals of the dependent variable. It applies to evolution equations invariant under Lie point symmetries leaving the temporal variable invariant. We construct inequivalent realizations of two and threedimensional Lie algebras leading to evolution equations admitting quasilocal symmetries. Finally, we generalize the approach in question for the case of an arbitrary system of evolution equations in two independent variables. Keywords: Quasilocal symmetry, nonlinear evolution equation, Lie algebra. MSC: 35Q80, 58Z05, 58J70 [ Fulltextpdf (180 KB)] for subscribers only. 