Group-theoretical framework for potential symmetries of evolution equations

We develop algebraic approach to the problem of classification of potential symmetries of nonlinear evolution equations. It is essentially based on the recently discovered fact [R. Zhdanov, J. Math. Phys. 50, 053522 (2009)], that any such symmetry is mapped into a contact symmetry. The approach enables using the classical results on classification of contact symmetries of nonlinear evolution equations by Sokolov and Magadeev to classify evolution equations admitting potential symmetries. We construct several examples of new nonlinear fourth-order evolution equations admitting potential symmetries. Since the symmetries obtained depend on nonlocal variables, they cannot be derived by the infinitesimal Lie approach.