= Characteristic direction
For a scalar second-order <partial differential equation> in two variables, a tangent direction along which <Cauchy data> fail to determine the highest transverse derivative through the equation. For principal part $Au_{xx}+2Bu_{xy}+Cu_{yy}$, a tangent $(dx,dy)$ is characteristic exactly when $A(dy)^2-2B\,dx\,dy+C(dx)^2=0$. Equivalently its conormal annihilates the <principal symbol>. A <hyperbolic partial differential equation> has two distinct real characteristic directions at each point.
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