Two methods of integrating Monge-Ampère’s equations. II
HTML articles powered by AMS MathViewer
- by Michihiko Matsuda PDF
- Trans. Amer. Math. Soc. 166 (1972), 371-386 Request permission
Abstract:
Generalizing the notion of an integrable system given in the previous note [2], 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 $(n + 1)$th Laplace invariant ${H_n}$ 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.References
- J. Clairin, Sur la transformation d’Imschenetsky, Bull. Soc. Math. France 41 (1913), 206–228 (French). MR 1504711, DOI 10.24033/bsmf.928
- Michihiko Matsuda, Two methods of integrating Monge-Ampère’s equations, Trans. Amer. Math. Soc. 150 (1970), 327–343. MR 261135, DOI 10.1090/S0002-9947-1970-0261135-5
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 166 (1972), 371-386
- MSC: Primary 35L60
- DOI: https://doi.org/10.1090/S0002-9947-1972-0312084-7
- MathSciNet review: 0312084