Diffraction by an impedance strip I. Reducing diffraction problem to Riemann-Hilbert problems

A 2D problem of acoustic wave scattering by a segment bearing impedance boundary conditions is considered. In the current paper (the first part of a series of two) some preliminary steps are made, namely, the diffraction problem is reduced to two matrix Riemann-Hilbert problems with exponential growth of unknown functions (for the symmetrical part and for the antisymmetrical part). For this, the Wiener–Hopf problems are formulated, they are reduced to auxiliary functional problems by applying the embedding formula, and finally the Riemann-Hilbert problems are formulated by applying the Hurd’s method. In the second part the Riemann-Hilbert problems will be solved by a novel method of OE-equation.