Solution of a singular integral equation in a double interval arising in the theory of water waves

Abstract

This paper is concerned with a straightforward method of solving a singular integral equation in a double interval arising in the linear theory of water waves. The kernel of the integral equation involves a combination of logarithmic and Cauchy type singularity. The integral equation is solved by utilizing the solution of a singular integral equation of first kind with a Cauchy type kernel in (0,∞) and in a finite interval.