Integrable Maxwellian Evolution and Geometric Phases in Multiplicative Euclidean Space
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, cilt.65, sa.5, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 65 Sayı: 5
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s10773-026-06342-0
- Dergi Adı: INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, INSPEC, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO), Engineering Source (EBSCO), Technology Collection (ProQuest)
- Anahtar Kelimeler: Anholonomic coordinates, Dini surface, Geometric phase, Integrable systems, Maxwellian curve evolution, Multiplicative differential geometry
- Ankara Üniversitesi Adresli: Evet
Özet
This study investigates the geometric dynamics of electromagnetic wave propagation along optical fibers within a non-Newtonian (multiplicative) differential geometry framework. Modeling the optical fiber as a space curve in multiplicative Euclidean 3-space, we construct a specialized anholonomic coordinate system associated with the multiplicative Frenet frame. Within this setup, we reformulate Maxwell's equations to derive a novel set of Maxwellian curve evolution equations. We rigorously analyze the polarization evolution of the electric and magnetic fields, establishing explicit relationships between the non-Newtonian Berry phase, Rytov parallel transport, and Fermi-Walker transport laws in both the normal (nu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ u $$\end{document}) and binormal (beta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}) directions. Furthermore, we demonstrate that the derived evolution equations satisfy the Mainardi-Gauss-Codazzi-type compatibility conditions. This geometric formulation reveals a deep intrinsic connection between electromagnetic wave propagation and integrable systems, as exemplified by the emergence of the sine-Gordon equation and the Dini surface geometry in the context of constant negative curvature.