ABSTRACT
In this chapter we have presented the methods of solution of certain special forms of a pair of coupled singular integral equations of Carleman type occurring in the study of scattering of surface water wave problems (cf. Gayen et al. (2006, 2007), Gayen and Mandal (2009)). The coupled singular integral equations under consideration are of the following special forms:
(9.1)
(9.2)
The specifi c forms of the known function ( )a x which occurs in the study on water wave problems (cf. Gayen et al (2006, 2007), Gayen and Mandal (2009)) are
and
9.1 THE CARLEMAN SINGULAR INTEGRAL EQUATION
The Carleman singular integral equation over a semi-infi nite range given by
also occurs in the study of water wave problems (cf. Chakrabarti (2000)) and its solution can be obtained by reducing it to an appropriate Riemann Hilbert problem. Its method of solution is briefl y described below.
