Bidirectional and unidirectional spectral representations for the scalar wave equation

• Main Author: Koutoumbas, Anastasios M.
• Other Authors: Electrical Engineering
• Format: Others
• Language: en
• Published: Virginia Tech 2014
• Subjects: LD5655.V855 1990.K687; Cauchy problem > Numerical solutions > Research
• Online Access: http://hdl.handle.net/10919/41904; http://scholar.lib.vt.edu/theses/available/etd-04072009-040420/

<p>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.</p> === Master of Science