Exterior Analysis

9.6 The Method of Generalised Characteristics

We have seen in Sec. 9.2 that the solution of a first order non-linear partial differential equation can be constructed by means of characteristics starting from a given initial submanifold. We shall now try to generalise this method by employing isovectors of the ideal associated with a system of partial differential equations. Let us denote the n = n + D number of local coordinates of the contact manifold Consider a vector field We know that its integral curves are obtained as solutions of the following ...