Rank two prolongations of second-order PDE and geometric singular solutions

2012/10/17 by Takahiro Noda, Noda, Takahiro, Kazuhiro Shibuya +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #math.DG

paper · pdf · doi:10.48550/arxiv.1210.4735

arxiv created 2012/10/17 · openalex publication_date 2012/10/17 · arxiv updated 2012/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this present paper, 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.

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