Nonlinear evolutions of electromagnetic flows in de Sitter 2-space

Abstract

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-solitonicmagnetic 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-solitonicmagnetic 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.