Two methods of integrating Monge-Ampère's equations. II
Abstract: Generalizing the notion of an integrable system given in the previous note , we shall define an integrable system of higher order, and obtain the following results:
1. A linear hyperbolic equation is solved by integrable systems of order n if and only if its th Laplace invariant vanishes.
2. An equation of Laplace type is solved by integrable systems of the second order if and only if the transformed equation by the associated Imschenetsky transformation is solved by integrable systems of the first order.
-  J. Clairin, Sur la transformation d’Imschenetsky, Bull. Soc. Math. France 41 (1913), 206–228 (French). MR 1504711
-  Michihiko Matsuda, Two methods of integrating Monge-Ampère’s equations, Trans. Amer. Math. Soc. 150 (1970), 327–343. MR 0261135, https://doi.org/10.1090/S0002-9947-1970-0261135-5
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Keywords: Monge-Ampère's equation, Laplace invariant, integrable system, Bäcklund transformation, Imschenetsky transformation
Article copyright: © Copyright 1972 American Mathematical Society