Symmetry Drivers and Formal Integrals of Hyperbolic Systems of Equations

In this paper, we consider symmetry drivers (i.e., operators that map arbitrary functions of one of independent variables into symmetries) and formal integrals (i.e., operators that map symmetries to the kernel of the total derivative). We prove that a hyperbolic system of partial differential equations has a complete set of formal integrals if and only if it admits a complete set of symmetry drivers. This assertion is also valid for difference and differential-difference analogs of scalar hyperbolic equations.