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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

The stability of particle-like solutions of some non-linear field equations

Anderson, David Lessells Thomson January 1969 (has links)
The object of this thesis is to examine the stability of particle-like solutions of the nonlinear field equation ▽2Ψ - 1/c2 δ2Ψ/δt2 = K2Ψ –μ2 ΨΨ*Ψ+λ(ΨΨ*)2Ψ with the particular form of time-dependence Ψ = φ (r) e − lwt Initially our interest is concentrated on the case λ = 0. We begin the analysis by finding spherically symmetric particle-like solutions, and then examining the stability of the lowest-order solution by first- order perturbation theory. Direct perturbation methods are then considered. This solution is found to be highly unstable whether it is time-independent (ω = 0) or not (ω ≠ 0). The more general case λ ≠ 0 is next discussed. Particle-like solutions are found to exist in this case for -∞ < λ (K2 - w2/c2) μ4 < 3/16 On examining the stability of the lowest-order solutions of this generalised field equation, it is found that for correct choice of the field parameters stable time-dependent solutions can exist, some of which can also have the attractive feature that their energy density is positive definite. We conclude by considering some methods of extending the theory.

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