Point and Potential Symmetries of Partial Differential Equations

It is generally accepted that point and potential symmetries of second order partial differential equations (the latter calculated as point symmetries of an equivalent system of partial differential equations) can be different. In this paper we present results which show that by extending point symmetries to include nonlocal variables, point and potential symmetries of second order partial differential equations can be obtained simultaneously. This is proven for a class of evolutionary and nonlinear wave equations. Illustrative examples are considered