On binary differential equations

Bruce, J.W. and Tari, F. (1995) On binary differential equations. Nonlinearity, 8 (2). pp. 255-271. ISSN 0951-7715 DOI https://doi.org/10.1088/0951-7715/8/2/008

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In this paper we give the local classification of solution curves of binary differential equations a(x,y)dy2+2b(x,y)dxdy+c(x,y)dx2=0 at points at which the discriminant function b2-ac has a Morse singularity. We also discuss the formal reduction of such equations to some normal form. The results determine the topological structure of asymptotic curves on a smooth surface with a flat umbilic, the principal curves at general umbilics, and asymptotic curves at cross-cap points of an otherwise smooth surface.

Item Type: Article
Subjects: Q Science > QA Mathematics
Date Deposited: 12 Jan 2011 11:38
URI: http://repository.edgehill.ac.uk/id/eprint/2202

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