Solution of a singular integral equation involving two intervals arising in the theory of water waves

Abstract

Using the well-known inverse of the Cauchy singular integral operator on a single interval along with certain standard results associated with singular integrals, the general solution of a singular integral equation in a double interval arising in the linear theory of water waves, whose kernel involves a logarithmic as well as a Cauchy type singularity, has been obtained. The solutions are found to agree with the known ones.