Formal integrals and Noether operators of non-Lagrangian nonlinear hyperbolic systems admitting a rich set of symmetries

The paper is devoted to hyperbolic (generally speaking, non-Lagrangian and nonlinear) partial differential systems possessing a full set of differential operators that map any function of one independent variable into a symmetry of the corresponding system. We demonstrate that a system has the above property if and only if the system admits a full set of formal integrals (i.e. differential operators which map any symmetry into an integral of the system). As a consequence, such systems have both direct and inverse Noehter operators (in terms of a work of B. Fuchssteiner and A.S. Fokas who have used these terms for operators that map cosymmetries into symmetries and back).