On a Lie Group Characterization of Quasi-Local Symmetries of Nonlinear Evolution Equations

We develop an efficient algebraic approach to classifying nonlinear evolution equations in one spatial dimension that admit non-local transformation groups (quasi-local 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 three-dimensional Lie algebras leading to evolution equations admitting quasi-local symmetries.Finally, we generalize the approach in question for the case of an arbitrary system of evolution equations in two independent variables.