Title page for ETD etd-04072009-040420
|Type of Document
||Koutoumbas, Anastasios M.
||Bidirectional and unidirectional spectral representations for the scalar wave equation
||Master of Science
|Besieris, Ioannis M.
|Brown, Gary S.
|Kim, Jong Uhn
|Date of Defense
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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