Classification of local and nonlocal symmetries of fourth-order nonlinear evolution equations

In this paper, we consider the group classification of local and quasi-local symmetries for a general fourth-order evolution equations in one spatial variable. Following the approach developed in [26], we construct all inequivalent evolution equations belonging to the class under study which admit either semi-simple Lie groups or solvable Lie groups. The obtained lists of invariant equations (up to a local change of variables) contain both the well-known equations and a variety of new ones possessing rich symmetry. Based on the results on the group classification for local symmetries, the group classification for quasi-local symmetries of the equations is also given.