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Summary

This study presents a new method for deriving spectral functional equations and generalized Wiener-Hopf equations (GWHEs) for wave motion in angular regions. These GWHEs are applicable to electromagnetics and arbitrary linear media.

Keywords:
Wiener–Hopf methodelectromagneticsintegral equationsspectral domainwave motionwedge

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Area of Science:

  • Electromagnetics
  • Wave Propagation
  • Mathematical Physics

Background:

  • Wave motion in angular regions presents challenges in analysis.
  • Existing methods may not cover arbitrary linear media or sources at infinity.

Purpose of the Study:

  • Introduce a general method to deduce spectral functional equations.
  • Derive generalized Wiener-Hopf equations (GWHEs) for wave motion.
  • Apply the theory to electromagnetic wave problems.

Main Methods:

  • Solving first-order vector differential equations to model wave motion.
  • Applying boundary conditions to functional equations to obtain GWHEs.
  • Developing a general theory for GWHEs.

Main Results:

  • A general method for deducing spectral functional equations is established.
  • Generalized Wiener-Hopf equations (GWHEs) are derived for wave motion in angular regions.
  • The validity of GWHEs in electromagnetic applications is demonstrated.

Conclusions:

  • The proposed method provides a general framework for spectral functional equations and GWHEs.
  • The derived GWHEs are applicable to wave motion in arbitrary linear homogeneous media.
  • This work validates GWHEs for electromagnetic applications and suggests future extensions.