Second-order generalized Monge--Amp\`ere equations on a plane and its geometric singular solutions
Abstract
In the present paper, we study some generalized Monge--Amp\`ere equations in terms of special exterior differential systems on a jet space. Moreover, we construct geometric singular solutions of the generalized Monge--Amp\`ere equations by using the method of Cauchy characteristics. Furthermore, we give criteria for geometric singular solutions to be right-left equivalent to the cuspidal edge, swallowtail and butterfly.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.