Wave Propagation and Diffraction

This book presents two distinct aspects of wave dynamics - wave propagation and diffraction - with a focus on wave diffraction. The authors apply different mathematical methods to the solution of typical problems in the theory of wave propagation and diffraction and analyze the obtained results. The rigorous diffraction theory distinguishes three approaches: the method of surface currents, where the diffracted field is represented as a superposition of secondary spherical waves emitted by each element (the Huygens-Fresnel principle); the Fourier method; and the separation of variables and Wiener-Hopf transformation method.

Chapter 1 presents mathematical methods related to studying the problems of wave diffraction theory, while Chapter 2 deals with spectral methods in the theory of wave propagation, focusing mainly on the Fourier methods to study the Stokes (gravity) waves on the surface of inviscid fluid. Chapter 3 then presents some results of modeling t

Lastly, it provides insights into directions for further developing the wave diffraction theory.