Multiple integral equations arising in the theory of water waves

A quick method of solution for multiple integral equations which are defined over a partition consisting of three intervals of the positive axis and whose kernel is the combination of trigonometric functions has been explained. The solution procedure can be extended to deal with similar integral equations defined over any finite partition of the positive axis. To represent the solution uniquely, certain solvability criteria are obtained in terms of the forcing functions involved. Limiting cases of dual integral equations over two disjoint intervals are discussed.