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A symmetric Riemann-Hilbert problem for order-4 vectors in diffraction theory. (English) Zbl 1205.78021
The author first analyzes a special set of \(n\times n\) matrices that allows for the Wiener-Hopf factorization. The procedure was then applied to find a closed form solution of a diffraction problem for an electromagnetic field induced by a harmonic electric line current in space bounded by two orthogonal semi-infinite plane-boundaries of given electric and magnetic properties. Finally, the performed method of solving the governing order-4 Riemann-Hilbert problem was extended to the case of \(n\times n\) matrices.

MSC:
78A45 Diffraction, scattering
35Q15 Riemann-Hilbert problems in context of PDEs
15A99 Basic linear algebra
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