Wave scattering by a sloping beach of an arbitrary angle. Revisited: regular solution

In this paper, we revisit the classic problem of a wave field on a sloping beach of an arbitrary angle and propose a general approach that allows the computation of regular solutions of the problem regardless of the angle. We use the Mellin-transform technique, reducing the problem to singular integral equations with fixed-point singularities of a special kind. Exact formulas are provided for the reflection coefficient, phase shift and wave surge at the shoreline. We demonstrate the efficiency of the proposed approach in the frequency domain and use these results to compute time-dependent solutions. We compare our results with those known from the literature.