Title page for ETD etd-04072009-040420


Type of Document Master's Thesis
Author Koutoumbas, Anastasios M.
URN etd-04072009-040420
Title Bidirectional and unidirectional spectral representations for the scalar wave equation
Degree Master of Science
Department Electrical Engineering
Advisory Committee
Advisor Name Title
Besieris, Ioannis M. Committee Chair
Brown, Gary S. Committee Member
Kim, Jong Uhn Committee Member
Keywords
  • Cauchy problem
Date of Defense 1990-06-13
Availability restricted
Abstract

The Cauchy problem associated with the scalar wave equation in free space is used as a vehicle for a critical examination and assessment of the bidirectional and unidirectional spectral representations. These two novel methods for synthesizing wave signals are distinct from the superposition principle underlying the conventional Fourier method and they can effectively be used to derive a large class of localized solutions to the scalar wave equation. The bidirectional spectral representation is presented as an extension of Brittingham's ansatz and Ziolkowski's Focus Wave Mode spectral representations. On the other hand, the unidirectional spectral representation is motivated through a group-theoretic similarity reduction of the scalar wave equation.

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