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Functional and Integral Equations for Strip Diffraction (Neumann Boundary Problem)

Functional and Integral Equations for Strip Diffraction (Neumann Boundary Problem)

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The previous chapters approximated higher-order edge waves. Now, using strips as an example, this chapter will study the properties of these waves in more detail. There are several reasons that prompt us to investigate these problems. Presently, there is significant interest in studying the exact structure of weak signals reflected from various objects. Clearly, their physical nature is related to higher-order edge waves. Besides, diffraction not only from isolated scatterers but also from groups of bodies, is of important practical interest. Referring to duality theory, diffraction from a strip is equivalent to a slot formed by two half-planes and is a special case of diffraction from two bodies. It is evident that the diffraction interaction of two half-planes is also caused by edge waves. Understanding strip diffraction is useful for studying these issues.

Chapter Contents:

  • 8.1 Asymptotic Solutions for Strip Diffraction
  • 8.2 Symmetry of Edge Waves
  • 8.3 Formulation and Solution of the Functional Equations
  • 8.4 Scattering Pattern and the Edge Wave Equation
  • 8.5 Infinite Series for the Current and Its Properties
  • 8.6 Convergence of Infinite Series for the Current
  • 8.7 Integral Equation for the Current and Schwarzschild's Solution
  • 8.7.1 Integral Equation Resulting from the Solution of Functional Equations (8.3.10)
  • 8.7.2 Integral Equation Resulting from Schwarzschild's Solution
  • 8.7.3 Equivalency of Kernels K(x,z) and (x,z)
  • 8.8 Transformation of Equation (8.5.2) into Equation (8.5.10)

Inspec keywords: boundary-value problems; integral equations; strips; diffraction; electromagnetic wave propagation; functional equations; duality (mathematics)

Other keywords: Neumann boundary problem; strip diffraction; higher-order edge waves; duality theory; functional equation; integral equation

Subjects: Mathematical analysis; Electromagnetic waves: theory; Electromagnetic wave propagation; Function theory, analysis

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