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Item Riemann–Hilbert approach to the elastodynamic equation: half plane(Springer, 2021-05) Its, Alexander; Its, Elizabeth; Mathematical Sciences, School of ScienceWe show, how the Riemann–Hilbert approach to the elastodynamic equations, which have been suggested in our preceding papers, works in the half plane case. We pay a special attention to the emergence of the Rayleigh waves within the scheme.