Monge systems

Every second order scalar equation in two independent variables can be formulated on a 7 dimensional equation manifold with a rank 4 contact distribution. For hyperbolic equations this distribution has two singular subsystems, called the Monge characteristics. The Monge characteristics determine the structure of the integral elements and give all integral manifolds a double foliation by characteristic curves. If each characteristic system has at least two first integrals then the equation is Darboux integrable.

For more information see:

• Lie's structural approach to PDE systems, by Olle Stormark. Contains information about the Monge characteristics and singular subsystems
• Vessiot structure for manifolds of (p,q)-hyperbolic type: Darboux integrability and symmetry, by Peter J. Vassiliou. Gives an introduction to the characteristic systems and Darboux integrability.

The Maple package MongeSystems calculated the characteristic systems of second order scalar equations and first order systems in two dependent and two independent variables. The package is available at the download page. You also need the other packages: MiscPTE, jetspte and VessiotJets.