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      Preface

      The theory of wave diffraction by wedges constitutes one of the fundamental problems in mathematical physics. Beyond the obvious applications to engineering and physics, this topic has generated – and continues to generate – new progress in the techniques of applied mathematics (e.g. the Sommerfeld–Malyuzhinets technique and the Kontorovich–Lebedev method), and applied physics (e.g. the geometrical theory of diffraction and the physical theory of diffraction).

      The scattering of wedge structures is of interest in the study of electromagnetic response/interaction of more complex, multiscale computational electromagnetic problems, using diffraction coefficients for modeling subdomains where high-frequency methods hold promise.

      This book, which is divided into two volumes, presents a general flexible, novel and powerful methodology for solving problems of electromagnetism in regions containing arbitrary wedge objects; this technique can be extended, as suggested, to different physics.

      The proposed technique is based on a generalization of the Wiener-Hopf (WH) technique that allows the study of complex canonical scattering problems.

      Research carried out during the past two decades has ordered and systematized the procedure, to obtain spectral equations and integral representations for complex problems to avoid redundancy.

      The purpose of this book is to present the application of the so-called generalized Wiener-Hopf technique (GWHT) to wedge scattering problems. This method often adopts very sophisticated mathematical methods; however, since the aim of the authors is to favor the acquisition of fundamental concepts in view of possible applications, they prefer to omit rigorous mathematical proofs for theory such as theorems. For all unproven mathematics, we refer to papers and books that are easily available.

      Due to the electrical engineering background of the authors, the two volumes are focused on electromagnetic applications. However all of the material is presented in such a way that extension to other physics and applied mathematical fields is straightforward; from applications in all areas of diffraction problems, such as acoustics, elasticity, aerodynamics, hydrodynamics and so on.

      Analogies between some resolved problems in electromagnetics and other areas of physics are reported. In particular, for example, the diffraction of a half-infinite crack in an elastic solid medium is described in detail.

      Before dealing with the applications to wedge problems, we present some useful remarks about the WH technique. First, the classical and consolidated method of solution of WH equations is founded on a deep knowledge of the properties of complex functions, which is based on the following classical steps: the multiplicative factorization of the kernel, the additive factorization (decomposition) of functions and the application of Liouville’s theorem.

      Second, in general, no WH problem is simple to study and solve. The formulation can be cumbersome to obtain and very specialized techniques are needed to

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