Tokyo Journal of Mathematics

Rank Two Prolongations of Second-order PDE and Geometric Singular Solutions

Takahiro NODA and Kazuhiro SHIBUYA

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Abstract

We study geometric structures of rank two prolongations of implicit second-order partial differential equations (PDEs) for two independent and one dependent variables and characterize the type of these PDEs by the topology of fibers of the rank two prolongations. Moreover, by using properties of these prolongations, we give explicit expressions of geometric singular solutions of second-order PDEs from the point of view of contact geometry of second order.

Article information

Source
Tokyo J. Math., Volume 37, Number 1 (2014), 73-110.

Dates
First available in Project Euclid: 28 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1406552432

Digital Object Identifier
doi:10.3836/tjm/1406552432

Mathematical Reviews number (MathSciNet)
MR3264515

Zentralblatt MATH identifier
1301.58002

Subjects
Primary: 58A15: Exterior differential systems (Cartan theory)
Secondary: 58A17: Pfaffian systems

Citation

NODA, Takahiro; SHIBUYA, Kazuhiro. Rank Two Prolongations of Second-order PDE and Geometric Singular Solutions. Tokyo J. Math. 37 (2014), no. 1, 73--110. doi:10.3836/tjm/1406552432. https://projecteuclid.org/euclid.tjm/1406552432


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