Geodesic
Hyperbolic Equations Admitting Differential Substitutions
Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 1, pp. 63-74

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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 $y$. 
@article{TMF_2001_127_1_a4,
     author = {S. Ya. Startsev},
     title = {Hyperbolic {Equations} {Admitting} {Differential} {Substitutions}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {63--74},
     publisher = {mathdoc},
     volume = {127},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_127_1_a4/}
}
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S. Ya. Startsev. Hyperbolic Equations Admitting Differential Substitutions. Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 1, pp. 63-74. http://geodesic.mathdoc.fr/item/TMF_2001_127_1_a4/