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Second-order generalized Monge--Ampère equations on a plane and its geometric singular solutions (2111.06695v2)
Published 12 Nov 2021 in math.DG
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.
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