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Burgers’ Equations in the Riemannian Geometry Associated with First-Order Differential Equations
Joint Authors
Source
Advances in Mathematical Physics
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-02-08
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
We construct metric connection associated with a first-order differential equation by means of the generator set of a Pfaffian system on a submanifold of an appropriate first-order jet bundle.
We firstly show that the inviscid and viscous Burgers’ equations describe surfaces attached to an ODE of the form dx/dt=u(t,x) with certain Gaussian curvatures.
In the case of PDEs, we show that the scalar curvature of a three-dimensional manifold encoding a system of first-order PDEs is determined in terms of the integrability condition and the Gaussian curvatures of the surfaces corresponding to the integral curves of the vector fields which are annihilated by the contact form.
We see that an integral manifold of any PDE defines intrinsically flat and totally geodesic submanifold.
American Psychological Association (APA)
Ok Bayrakdar, Z.& Bayrakdar, T.. 2018. Burgers’ Equations in the Riemannian Geometry Associated with First-Order Differential Equations. Advances in Mathematical Physics،Vol. 2018, no. 2018, pp.1-8.
https://search.emarefa.net/detail/BIM-1119273
Modern Language Association (MLA)
Ok Bayrakdar, Z.& Bayrakdar, T.. Burgers’ Equations in the Riemannian Geometry Associated with First-Order Differential Equations. Advances in Mathematical Physics No. 2018 (2018), pp.1-8.
https://search.emarefa.net/detail/BIM-1119273
American Medical Association (AMA)
Ok Bayrakdar, Z.& Bayrakdar, T.. Burgers’ Equations in the Riemannian Geometry Associated with First-Order Differential Equations. Advances in Mathematical Physics. 2018. Vol. 2018, no. 2018, pp.1-8.
https://search.emarefa.net/detail/BIM-1119273
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1119273