Singularities of Cauchy data, characteristics, cocharacteristics and integral cobordism
type: Item
instance of: scholarly article
title: Singularities of Cauchy data, characteristics, cocharacteristics and integral cobordism
zbMATH Open document ID: 0808.58039
DOI: 10.1016/0926-2245(94)00017-4
published in: Differential Geometry and its Applications
publication date: 1995-03-16T00:00:00Z
review text: A generalization of the classical concept of characteristics for partial differential equations (PDE) is given in the framework of the geometric formal theory for PDEs. In particular, it is given a relation between singularities of Cauchy data and characteristics in order to obtain integral manifolds (solutions) generated by means of characteristics. In this direction it is shown that to any PDE we can associate a ``dual'' equation having the same characteristics. These equations can be related by means of a sort of Bäcklund transformation. Furthermore, a criterion that relates characteristics and integral cobordism (or quantum cobordism) is given. Also a relation between quantum cobordism in nonlinear PDE's and Green's functions is given.
Mathematics Subject Classification ID: 58J32
Mathematics Subject Classification ID: 58J72
Mathematics Subject Classification ID: 58H99
zbMATH DE Number: 701735
zbMATH Keywords: geometry of partial differential equations
zbMATH Keywords: cobordism in PDEs
zbMATH Keywords: Bäcklund transformation
Wikidata QID: Q115362622
author: Valentin Lychagin
author: Agostino Prástaro
MaRDI profile type: Publication
full work available at URL: 0926-2245(94)00017-4
OpenAlex ID: W1968517923
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description: scientific article; zbMATH DE number 701735