inhomogeneous integral equation

With the help of the Green's function in bispherical coordinates, it is shown that for any wavenumber, the scattered wave satisfies an inhomogeneous integral equation in two variables.

For two-dimensional scattering, if the geometry of the scatterers is simple enough, the Laplace equation with the prescribed boundary conditions on the surface of the scatterers is separable in a certain coordinate system, then one can write the solution of the wave equation as an inhomogeneous integral equation.