Tokyo Journal of Mathematics
- Tokyo J. Math.
- Volume 37, Number 1 (2014), 73-110.
Rank Two Prolongations of Second-order PDE and Geometric Singular Solutions
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.
Tokyo J. Math., Volume 37, Number 1 (2014), 73-110.
First available in Project Euclid: 28 July 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 58A15: Exterior differential systems (Cartan theory)
Secondary: 58A17: Pfaffian systems
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