1998/04/08 by Paul J. Werbos, Werbos, Paul J. · 1 citation
Physics and Astronomy · #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS) #Quantum Mechanics and Applications #Quantum chaos and dynamical systems #Radioactive Decay and Measurement Techniques #nlin.PS #patt-sol
paper · pdf · doi:10.48550/arxiv.patt-sol/9804003
60p., no figs, 200+ eqs. Companion to "Can 'soliton' attractors exist in realistic 3+1-D Conservative Systems", Chaos Solitons and Fractals, in press
arxiv created 1998/04/08 · openalex publication_date 1998/04/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper provides mathematical details related to another new paper which suggests: (1) new approaches to the analysis of soliton stability; (2) families of Lagrangian field theories where solitons might possibly exist even without topological charge; (3) alternative approaches to quantizing solitons, with testable nuclear implications. This paper evaluates the possibility of strong energy-minimizing states in four families of systems, two promising and two not promising. In these examples, it presents new methods for second-order stability analysis, and analyzes persistent multifurcation. Section 6 presents three alternative formalisms for quantizing solitons (topological or nontopological), all of which have major implications for the foundations of quantum theory: (1) the standard formalism, based on functional integration, reinterpreted as an imaginary Markhov Random Field (iMRF) across time and space, with parallels to fuzzy logic; (2) two radically conservative formalisms, consistent with the core of Einstein's vision, based on a true MRF model. Bell's Theorem, bosonization, time-symmetry and macroscopic asymmetry are discussed, along with some testable alternative possibilities and heresies, like nonDoppler redshift.