A water wave scattering problem: Revisited

The problem of water wave scattering by a thin vertical wall with a gap submerged in deep water is studied using singular integral equation formulation. The corresponding boundary value problem is reduced to a Cauchy type singular integral equation of first kind in two disjoint intervals where the unknown function satisfying the integral equation has square root zero at the end points of the two intervals. In this case the solution exists if the forcing function satisfies two solvability conditions. The reflection coefficient is determined here using the solvability conditions without solving the integral equation and also the boundary value problem.