Geodesic
The Cauchy problem for hyperbolic Monge--Amp\`ere equations
Izvestiya. Mathematics , Tome 43 (1994) no. 1, pp. 161-178

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This article is devoted to Monge–Ampère equations with two independent variables. Here a definition of hyperbolicity is formulated that permits an extension of the class of hyperbolic Monge–Ampère equations and the inclusion of a number of equations with multiple haracteristics in this class. The definition is proved to be invariant under changes of variables. Equations hyperbolic in the sense of the new definition are reduced to corresponding systems in Riemann invariants. The existence and uniqueness of a local solution of the Cauchy problem is proved on the basis of this reduction. 
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     author = {D. V. Tunitsky},
     title = {The {Cauchy} problem for hyperbolic {Monge--Amp\`ere} equations},
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D. V. Tunitsky. The Cauchy problem for hyperbolic Monge--Amp\`ere equations. Izvestiya. Mathematics , Tome 43 (1994) no. 1, pp. 161-178. http://geodesic.mathdoc.fr/item/IM2_1994_43_1_a9/