https://doi.org/10.1140/epjp/s13360-023-04505-0
Regular Article
Nonlinear evolutions of electromagnetic flows in de Sitter 2-space
Department of Mathematics, Muş Alparslan University, 49100, Muş, Turkey
a rcdemirkol@gmail.com, rc.demirkol@alparslan.edu.tr
Received:
20
March
2023
Accepted:
20
September
2023
Published online:
8
October
2023
In this study, we derive novel pseudo-spherical frames in de Sitter 2-space. We obtain new connections for the nonlinear evolution of curves associated with the complex modified Korteweg–de Vries (cmKDV
) equation, generalized Korteweg–de Vries (gKDV) equation, and others. We then describe some pseudo-solitonic surfaces swept out by these novel classes of nonlinearly moved curves as time evolves. Moreover, we observe the relationship between pseudo-solitonic structures and the magnetic trajectories of charged particles. Thus, we obtain a novel class of complex and non-complex evolution of the electromagnetic flows of the associated pseudo-solitonic magnetic curves. We also focus on the particular case in which the electromagnetic field of a linearly polarized light wave coupling into the optical fiber is investigated based on the inner geometric features of the novel pseudo-spherical frames in de Sitter 2-space. Finally, we investigate the corresponding energy functional to compute the Hashimoto-like transformed energy of pseudo-solitonic curves, pseudo-solitonic magnetic curves, and pseudo-solitonic electromagnetic curves. Overall, the derived results in this study could have potential applications improving the design and performance of optical fibers, developing new models for electromagnetic flows, advancing the understanding of pseudo-solitonic structures.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
