Hyperbolic Equations Admitting Differential Substitutions

We show that the first $n-1$ Laplace invariants of a scalar hyperbolic equation obtained from an equation of the same form under a differential substitution of the $n$th order have a zeroth order with respect to one of the characteristics. It follows that all Laplace invariants of an equation admitting substitutions of an arbitrarily high order must have a zeroth order. Three special cases of such equations are considered: those admitting autosubstitutions, those obtained from a linear equation by a differential substitution, and those with solutions depending simultaneously on both an arbitrary function of $x$ and an arbitrary function of $y$.