Duality and implicit differential equations

Bruce, J.W. and Tari, F. (2000) Duality and implicit differential equations. Nonlinearity, 13 (3). pp. 791-811. ISSN 0951-7715 DOI https://doi.org/10.1088/0951-7715/13/3/315

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Abstract

We prove some duality results concerning various types of implicit differential equations where F is a smooth function. We show, for instance, that the well folded singularities are self-dual. The results are used to deduce some geometric properties of surfaces in 3-space. So, for example, there are three flecnodal curves at an elliptic flat umbilic and one at a hyperbolic flat umbilic. These curves are tangent to the separatrices of the binary differential equation determining the asymptotic lines.

Item Type: Article
Subjects: Q Science > QA Mathematics
Date Deposited: 17 Jan 2011 12:22
URI: http://repository.edgehill.ac.uk/id/eprint/2226

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