Burgers' Equations in the Riemannian Geometry Associated with First-Order Differential Equations
Küçük Resim Yok
Tarih
2018
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Hindawi Ltd
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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.
Açıklama
Anahtar Kelimeler
Kaynak
Advances in Mathematical Physics
WoS Q Değeri
Q3
Scopus Q Değeri
Q3
