Browsing by Author "Luke, Jon C."

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Interaction of Solitons with the Electromagnetic Field in Classical Nonlinear Field Models
    (InTechOpen, 2018) Luke, Jon C.
    Solitary waves and solitons are briefly discussed in their historical context, especially regarding the motivation to use solitons for particle models in the nonlinear Klein-Gordon (NKG) equation. Conservation equations for charge, energy, and momentum follow from Noether’s theorem in the usual way, and the NKG equation can be coupled to Maxwell’s equations in the standard, gauge invariant manner. A recently proposed model is summarized in which two NKG equations are coupled to the electromagnetic field. In that model, solitons mimic the dynamical behavior of electrons and protons. A new result is then presented that follows from that model. Although the model is purely classical, it turns out that the arc spectrum of hydrogen is emitted into the electromagnetic field when small oscillations of one Klein-Gordon equation occur in the vicinity of a proton-like soliton. It is perhaps unexpected that a purely classical model can exhibit behavior suggestive of a phenomenon that is generally presumed to occur only in a quantum-mechanical context. Because of the way in which that result occurs, however, it is not clear whether there is any possible relevance to the actual physical phenomenon.
  • Thumbnail Image
    Item
    A Note on the Use of the Nonlinear Dirac Equation for Soliton Particle Models
    (2022-05) Luke, Jon C.
    When nonlinear Dirac equations are to be used in classical soliton models, it is essential that certain paradoxical properties of spinors be avoided. This result can be achieved if Dirac’s equation is formulated in a slightly different way, where the dependent variable is a matrix rather than a column vector. It is helpful to understand the change in the context of a Clifford algebra.
  • Thumbnail Image
    Item
    A Proposed Model in which Solitons Exhibit Electron and Proton-like Behavior
    (De Gruyter, 2016-05) Luke, Jon C.; Department of Mathematical Sciences, School of Science
    A classical model is proposed in which two nonlinear Klein–Gordon fields interact via the electromagnetic field. Scaling is such that solitons in the two fields can be interpreted as electrons and protons, respectively. Even though the masses are very different, the magnitude of the charge of the electron-like soliton is the same as that of the proton-like soliton. Attraction and repulsion occur in the desired way through the interaction with the electromagnetic field.