1. Identify Cauchy Data in Characteristic Form

By means of the derivative $\frac{d\psi(s)}{ds}$ the Cauchy data

$$\left. \begin{array}{ccl} \displaystyle \frac{d\psi (s)}{dn} &= &... ...\frac{d\psi}{dy} \end{array} \right\}~~\textrm{at}~~(x,y)=(\xi(s) ,\eta(s) )\,.$$

determines the partial derivatives $\partial \psi/\partial x$ and $\partial \psi/\partial y$ . Alternatively, the known characteristics

$$u = u(x,y)$$

$$v = v(x,y)$$

also yield the partial derivatives $\partial \psi/\partial u$ and $\partial \psi/\partial v$ on the given curve.