The solution exact solution of the Helmholtz equation for the scattering of waves by a sphere is relatively straightforward and has been known since the time of Lord Rayleigh.

The exact solution of the wave equation for scattering of waves by a sphere is much trickier and has been dealt with in two relatively recent papers - here and here.

I have been trying to determine whether there exists an exact solution for the wave equation in the two-dimensional case, i.e. for a disk/cylinder. It is not mentioned in the recent papers I listed above for the case of the sphere, and I haven't been able to find anything despite an extensive search of the literature.

Does anyone know if an exact solution of the wave equation for the scattering of waves by a disk/cylinder exists, or is this still an open problem?