A rigorous approach to wave scattering by elliptic disks and related problems

An original approach to solve rigorously a class of wave scattering problems from thin elliptic disks is developed. Applying the boundary conditions, this non-traditional formulation first establishes two-dimensional dual integral equations with trigonometric function kernels for an unknown spectral density function. A parametrisation technique transforms these equations to “disk-like” one-dimensional dual integral equations with Bessel function kernels, that are solved by the Method of Regularisation. Finally, each problem is reduced to the solution of an infinite system of linear equations of the second kind for unknown coefficients arising from representation of the unknown spectral density function by a Neumann’s series.