平特五不中

Title: The variational bi-complex for systems of Quasi-linear hyperbolic PDE in three variables

Supervisor: 聽Niky Kamran, Mathemetics and Statistics, 平特五不中

Internal Examiner: 聽Professor Jean Christophe Nave,聽Mathemetics and Statistics, 平特五不中

Internal Member: 聽Professor Dmitry Jakobson,聽Mathemetics and Statistics, 平特五不中

External Members: 聽Professor Kaleem Siddiqi, School of Computer Science聽, 平特五不中聽

Abstract:

This thesis extends, to a class of systems of quasi-linear hyperbolic second oder PDE
in three variables, the geometric study of a single nonlinear hyperbolic PDE in the plane
as presented in [AK97]. The constrained variational bi-complex is introduced and used
to de ne form-valued conservation laws. A method for generating conservation laws
from solutions to the adjoint of the linearized system associated to a system of PDEs
is given. Finally, Darboux integrability for a system of three equations is de ned and a
method for generating in nitely many conservation laws for such systems is described.