Hidden symmetries for some classical field models

The problem of existence of hidden symmetries of an action invariant under spacetime transformations and internal transformations is studied. For this purpose transformations with generators being certain functions of coordinates are considered. Differential equations for these functions are obtained from the condition of invariance of the action. These equations are solved in two-dimensional case. It is obtained that coordinate transformations depend on fields and corresponding higher integrals are of the Noether character