\b[Characteristic.] The third-order <principal symbol> of $\partial_t-\partial_x^3$ is $-\nu_x^3$. The initial line has normal $(\nu_x,\nu_t)=(0,1)$, on which this symbol vanishes. Its evolution form does not make it non-characteristic in the ordinary total-order definition.

Solution

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

 Solution (source code)