Hidden symmetries for some classical field models

The existence of hidden symmetries for an action invariant with respect to space-time transformations $K$ and internal transformations $G$ is investigated. For this purpose transformations with generators that are functions of the coordinates are considered. For these functions, differential equations are obtained from the condition of invariance of the action. Solutions of these equations are found in the two-dimensional case. It is shown that the coordinate transformations depend on the fields and that the corresponding higher conserved quantities are of the Noether type.