= Noncharacteristic Cauchy data
{c}
{title2=$a\eta'-b\xi'\ne0$}
For $au_{x_1}+bu_{x_2}=c$ with data along $(\xi(s),\eta(s))$, the initial curve is noncharacteristic when its tangent is linearly independent of the projected characteristic vector $(a,b)$ evaluated at the initial value of $u$. The determinant is $a\eta'-b\xi'$, up to sign. For $C^1$ coefficients and data this permits the <inverse function theorem> to invert the local characteristic parametrization and gives a unique local <classical solution>.
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