Real part of the solution of Eq. (G.1) as a function of x in logarithmic scale computed numerically for various mesh resolutions. The number of points of the spatial discretization is set at N = 20 (green dashed line), N = 200 (blue dashed line), N = 2000 (pink dashed line), and N = 20 000 (cyan dashed line). These numerical solutions are compared to the analytical solution given by Eq. (129) (red line).