Dr Peter Vassiliou

Office: 11C8

Phone: (02) 6201 2623

Fax: (02) 6201 5231

Email: Peter.Vassiliou@canberra.edu.au

Mail:
11C8, Building 11
Faculty of Information Sciences and Engineering
University of Canberra, Bruce ACT 2601

Research Area

Peter has interests in differential equations, differential geometry and the interaction of these two fields with each other. The identification of geometric objects such as connections, metrics, symmetries, etc., associated to classes of differential equations, in order to illuminate the solutions is of particular interest.  This borderland between differential geometry and differential equations is now sometimes called the “geometry of differential equations” and builds on the work of pioneers such as Sophus Lie, Elie Cartan, Ernest Vessiot, Gaston Darboux and Edouard Goursat to name just a few. It includes topics such as symmetries, conservation laws, and equivalence problems. Peter’s work particularly explores those geometric structures capable of constructing explicit solutions to nonlinear differential equations such as the classical method of Darboux .

Recent Publications

Peter J. Vassiliou, “A constructive generalised Goursat normal form”, Differential Geometry and its Applications, 24 (2006), no. 4, 332-350

Peter J. Vassiliou, “Efficient construction of contact coordinates for partial prolongations”, Foundations of Computational Mathematics, 6, (2006), no. 3, 269-308

Peter J. Vassiliou, “An integrable system of partial differential equations on the special linear group”, ANZIAM Journal, 44 (2002), no. 1, 83-93

Peter J. Vassiliou, “Vessiot structure for manifolds of (p,q)-hyperbolic type: Darboux integrability and symmetry”, Transactions of the American Mathematical Society, 353 (2001), no. 5, 1705-1739

Peter J. Vassiliou, “Tangential characteristic symmetries and first order hyperbolic systems”, Applicable Algebra in Engineering, Communication and Computation, 11, (2001), no. 5, 377-395