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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