IJPAM: Volume 6, No. 2 (2003)

ODD-SYMPLECTIC GROUP IN FIRST ORDER
PARTIAL DIFFERENTIAL EQUATIONS

L. Sbano
Department of Mathematics and Statistic
University of Surrey
Guildford GU2 7XH, UNITED KINGDOM
e-mails: L.Sbano@eim.surrey.ac.uk, Sbano@maths.warwick.ac.uk


Abstract.In this paper it is shown that the characteristic vector field associated to the first order PDE:

\begin{displaymath}h(x,\nabla z(x))=0\mbox{ with $x\in\R^n$}\end{displaymath}

has the same form of an infinitesimal generator of an odd-symplectic transformation with contact Hamiltonian $h(x,p)$ on the level set $h=0$. We also study under which condition such PDE has a characteristic vector field commuting with a generator of an action of the odd-symplectic group.

Received: January 10, 2003

AMS Subject Classification: 53D05, 53D10, 35F05

Key Words and Phrases: symplectic geometry, contact geometry, first order PDE, theory of charcterics

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 6
Issue: 2