Nonlocal symmetries in two-field divergent evolutionary systems

We evaluate nonlocal symmetries for third-order exactly integrable two-field divergent evolutionary equations. These symmetries, regarded as evolutionary equations, commute with higher analogues of the underlying original equations and seem to be exactly integrable. By differentiating nonlocal systems and changing the variables, we obtain local hyperbolic systems and third-order nonevolutionary systems. We find a zero-curvature representation for some of the new systems.