Three anholonomy densities for three formulations with anholonomic coordinates with hybrid frame in R13

NE Gürbüz, R Myrzakulov, Z Myrzakulova - Optik, 2022 - Elsevier
In this paper, we present three formulations associated with the modified repulsive type
nonlinear Schrödinger NLS− equation in the h− lines and b− lines directions with respect to …

The evolution of electric field in pseudo-Galilean 3-space G13

NE Gürbüz - Optik, 2022 - Elsevier
In this paper, intrinsic derivatives in the pseudo-Galilean normal and pseudo-Galilean
binormal directions with respect to the Frenet frame in the pseudo-Galilean 3-space G 1 3 …

The evolution of an electric field with respect to the type-1 PAF and the PAFORS frames in R13

NE Gürbüz - Optik, 2022 - Elsevier
In this paper, after presenting the type-1 PAF and PAFORS frames in the Minkowski 3-space,
the evolution of an electric field associated with the nonlinear heat system and the nonlinear …

The null geometric phase along optical fiber for anholonomic coordinates

NE Gürbüz - Optik, 2022 - Elsevier
In this paper we study the change an electric field in the normal and binormal directions with
respect to the null Cartan frame via anholonomic coordinates in Minkowski 3-space. We …

Three geometric phases with the visco-Da Rios equation for the hybrid frame in R13

NE Gürbüz - Optik, 2021 - Elsevier
In this paper, three classes of curve evolution associated with the viscous modified nonlinear
Schrödinger equation in Minkowski 3-space are investigated. Following that, the hybrid …

Geometric phases for three cases of the electric field with new type Bishop frame in

DW Yoon, NE Gürbüz - … Journal of Geometric Methods in Modern …, 2022 - World Scientific
In this paper, we study geometric phases for an electric field in Minkowski 3-space. In
particular, we consider Bishop 2-type frames of a spacelike and a timelike curve in …

A new approach to the connections between moving curves and a family of complex KdV type systems

ZK Yüzbaşı - Mathematical Methods in the Applied Sciences, 2023 - Wiley Online Library
In this paper, we give a new approach to the existence of a connection between the
geometry of moving curves and the soliton equation for a family of complex KdV type …

Optical recursion systems for the Hasimoto map and optical applications with spherical frame

T Körpinar, A Sazak, Z Körpinar - Optik, 2022 - Elsevier
In this research, we analyze the Hasimoto map and some flow equations for spherical frame
(s-frame) in S 2 spherical space. Here, we first obtain Hasimoto map, which we call the s …

On the geometric dynamics of the charged point-particle propagated through the spherical optical fiber

T Körpinar, RC Demi̇rkol - Optik, 2022 - Elsevier
In this manuscript, we basically focus on the geometric dynamics of the charged particle
propagation through the spherical frame. To be able to investigate this process, we suppose …

Geometric Methodology for Analyzing Timelike Curve Flows in Minkowski Space

M Bektaş, DW Yoon, ZK Yüzbaşı - Results in Mathematics, 2024 - Springer
The present study introduces an innovative link between integrable equations and the
motion of timelike curves within a three-dimensional Minkowski space. This study aims to …