Evaluation of the solutions of Gaussian impulse propagation and diffraction on a corner $2\pi/n$

We consider two solutions of the $2\mathrm{D}$ wave equation, which can be used for verification of numerical methods. The first problem is wave propagation from Gaussian pulse. The second one is planar wave diffraction on a corner with the angle of $2\pi/n$. The solutions of both problems have integral representations. We offer a new method to calculate them.