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.
Citation
Takahiro NODA. Kazuhiro SHIBUYA. "Rank Two Prolongations of Second-order PDE and Geometric Singular Solutions." Tokyo J. Math. 37 (1) 73 - 110, June 2014. https://doi.org/10.3836/tjm/1406552432
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