The Riemann-Hilbert problem method in the theory of diffraction waves on screens of arbitrary cross section

Integral equations of the first kind are obtained for an open loop, and the closure of the loop is then accomplished. This allows the parametrization of the closed loop and analysis of the singular structure of the integral operator kernels. Also, by using the Fourier transformation, it is possible to reduce the integral equations to paired adder equations with a matrix perturbation whose implementation by the Riemann-Hilbert problem method yields an infinite system of algebraic equations of the second kind. (AIAA)