Wienner-Hopf technique and applications to some wave problems

In this thesis, two boundary-value problems with different geometries have been solved. Fundamental notions from complex analysis, Fourier transforms and the analyticity properties of Fourier transforms have been employed during the application of the Wiener-Hopf technique.The first problem considered is the Sommerfeld half-plane problem. An acoustic wave making an angle Theta with the x-axis is incident from the first quadrant of the x-y-plane on a barrier along the negative x-axis. Under given boundary conditions, the total potential arising due to the transmission, reflection and diffraction of the incident wave is analyzed at an arbitrary point of the plane. Jones? method is used in this analysis.In the second problem only the geometry differs in that there are now two semi-infinite barriers located at y=b and y=-b along the negative part of the x -axis, which now forms a channel. Imposing certain boundary conditions both along the walls of the channel and the positive x-axis, the total potential resulting from the transmission, reflection and diffraction of the incident wave is investigated at an arbitrary point of the plane.The Wiener-Hopf technique is used extensively to obtain the solution of both of the boundary-value problems.Keywords: Diffracted wave, Wiener-Hopf technique, Fourier transforms.