Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 105 / 1 / ii / Solution

Characteristic. The second-order principal symbol of $i{\partial }_t+{\partial }_x^2$ is ${\nu }_x^2$, which vanishes on the normal $(0,1)$. This uses total differential order, rather than an anisotropic convention that assigns different weights to time and space derivatives.