The <d'Alembert operator>[wave operator] has principal symbol
$$
p(\tau,\xi)=-\tau^2+|\xi|^2.
$$
The conormal to the initial plane is $dt$, and $p(dt)=-1\ne0$. The plane is therefore non-characteristic.

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 105 / 1 / b / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-105/1/b/i/solution