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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 the refraction of surf
Lastly, it provides insights into directions for further developing the wave diffraction theory.
Prof. Igor Selezov is a head of the Department of Hydrodynamics of Wave Processes at the Institute of Hydromechanics of the National Academy of Sciences of Ukraine (Kyiv, Ukraine). His scientific interests include wave processes in liquid and elastic media, wave diffraction, magnetohydrodynamics, wave biohydrodynamics. He is an author of more than 400 scientific publications and 12 monographs. Prof. Selezov is an Honoured Science and Engineering Worker of Ukraine, Foreign Member of GAMM (Gesellschaft für Angewandte Mathematik und Mechanik), a fellow of the National Committee on Theoretical and Applied Mechanics of Ukraine.
Prof. Yuriy Kryvonos is a member of the National Academy of Sciences of Ukraine. Hi is a vice-director of the Institute of Cybernetics of the National Academy of Sciences of Ukraine (Kyiv, Ukraine). His scientific interests include computer technologies, wave propagation and diffraction, identification of wave processes, controlling of dynami
Dr. Ivan Gandzha is a senior research fellow at the Department of Theoretical Physics at the Institute of Physics of the National Academy of Sciences of Ukraine (Kyiv, Ukraine). His scientific interests include the theory of nonlinear waves, solitons and chaos, nonlinear vibrations. He is an author of more than 30 scientific publications and one monograph. Dr. Gandzha is a member of the Editorial board of the Ukrainian Journal of Physics.
Some Analytical and Numerical Methods in the Theory of Wave Propagation and Diffraction .- Spectral Methods in the Theory of Wave Propagation.- Ray Method of Investigating the Wave Evolution over Arbitrary Topography.- Analytical and Numerical Solutions of Wave Diffraction Problems.- Wave Diffraction by Convex Bodies in Semibounded Regions.- Propagation and Evolution of Transient Water Waves.
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