Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Two methods of integrating Monge-Ampère's equations. II


Author: Michihiko Matsuda
Journal: Trans. Amer. Math. Soc. 166 (1972), 371-386
MSC: Primary 35L60
MathSciNet review: 0312084
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35L60

Retrieve articles in all journals with MSC: 35L60


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0312084-7
PII: S 0002-9947(1972)0312084-7
Keywords: Monge-Ampère's equation, Laplace invariant, integrable system, Bäcklund transformation, Imschenetsky transformation
Article copyright: © Copyright 1972 American Mathematical Society