Nondispersive Wave Packets.
Abstract
In this work, nondispersive wavepacket solutions to linear partial differential equations are investigated. These solutions are characterized by infinite energy content; otherwise they are continuous, nonsingular and propagate in free space without spreading out. Examples of such solutions are Berry and Balazs' Airy packet, MacKinnon's wave packet and Brittingham's Focus Wave Mode (FWM). It is demonstrated in this thesis that the infinite energy content is not a basic problem per se and that it can be dealt with in two distinct ways. First these wave packets can be used as bases to construct highly localized, slowly decaying, timelimited pulsed solutions. In the case of the FWMs, this path leads to the formulation of the bidirectional representation, a technique that provides the most natural basis for synthesizing Brittinghamlike solutions. This representation is used to derive new exact solutions to the 3D scalar wave equation. It is also applied to problems involving boundaries, in particular to the propagation of a localized pulse in a infinite acoustic waveguide and to the launchability of such a pulse from the opening of a semiinfinite waveguide. The second approach in dealing with the infinite energy content utilizes the bumplike structure of nondispersive solutions. With an appropriate choice of parameters, these bump fields have very large amplitudes around the centers, in comparison to their tails. In particular, the FWM solutions are used to model massless particles and are capable of providing an interesting interpretation to the results of Young's two slit experiment and to the waveparticle duality of light. The bidirectional representation provides, also, a systematic way of deriving packet solutions to the KleinGordon, the Schrodinger and the Dirac equations. Nondispersive solutions of the former two equations are compared to previously derived ones, e.g., the Airy packet and MacKinnon's wave packet.
 Publication:

Ph.D. Thesis
 Pub Date:
 1989
 Bibcode:
 1989PhDT.......126S
 Keywords:

 Physics: General