Maxwellian evolution equations along the uniform optical fiber

In this article, we firstly consider a new theory of spherical electromagnetic radiation density with antiferromagnetic spin of timelike spherical t -magnetic flows by the spherical Sitter frame in de Sitter space. Thus, we construct the new relationship between the new type electric and magnetic phases and spherical timelike magnetic flows de Sitter space 2.1 S Also, we give the applied geometric characterization for spherical electromagnetic radiation density. This concept also boosts to discover some physical and geometrical characterizations belonging to the particle. Moreover, the solution of the fractional-order systems are considered for the submitted mathematical designs. Graphical demonstrations for fractional solutions are presented to expression of the approach. The collected results illustrate that mechanism is relevant and decisive approach to recover numerical solutions of our new fractional equations. Components of performed equations are demonstrated by using approximately explicit values of physical assertions on received solutions. Finally, we constructthat electromagnetic fluid propagation along fractional optical fiber indicates an fascinating family of fractional evolution equation with diverse physical and applied geometric modelling in de Sitter space 2 1 S .

Section: Discussionmentioning

confidence: 99%

Optical electromagnetic radiation density spherical geometric electric and magnetic phase by spherical antiferromagnetic model with fractional system

Khalil

̈orpinar

2021

“…Then the parallel transportation law of polarization vectors − → E and − → B in the tangential direction along the optical fiber is verified by the Rytov law in the following way [6,10,16]…”

Section: Direction Along the Optical Fiber In Minkowski Spacementioning

confidence: 99%

“…Later, Haldane [5] proposed that these effects can be generalized for any arbitrary fiber trajectory without any restriction as in the earlier studies. Apart from previous researches [6][7][8][9][10], in Sec. 3, we propose that an electromagnetic wave acquires novel geometric phases in the normal and binormal directions during its propagation along the curved path in Minkowski space.…”

Section: Introductionmentioning

confidence: 99%

Maxwellian evolution equations along the uniform optical fiber in Minkowski space

Demi̇rkol²,

et al. 2020

We firstly discuss the geometric phase rotation for an electromagnetic wave traveling along the optical fiber in Minkowski space. We define two types of novel geometric phases associated with the evolution of the polarization vectors in the normal and binormal directions along the optical fiber by identifying the normal-Rytov parallel transportation law and binormal-Rytov parallel transportation law and derive their relationships with the new types of Fermi-Walker transportation law in Minkowski space. Then we describe a novel approach of solving Maxwell's equations in terms of electromagnetic field vectors and geometric quantities associated with the curved path characterizing the path uniform optical fiber by using the traveling wave transformation method. Finally, we investigate that electromagnetic wave propagation along the uniform optical fiber admits an interesting family of Maxwellian evolution equation having numerous physical and geometric applications for anholonomic coordinate system in Minkowski space

“…Sun established the connection between geometric invariants of the magnetic curves and magnetic normal binormal surfaces [13] . Körpınar et al investigated a new kind of evolution equation for electric and magnetic fields satisfying the Maxwell equations along with the uniform optical fiber in three-dimensional ordinary space and Minkowski space [14,15] .…”

Section: Introductionmentioning

confidence: 99%

Fractional solutions for the inextensible Heisenberg antiferromagnetic fow and solitonic magnetic flux surfaces in the binormal direction

Demi̇rkol²,

et al. 2021

Self Cite

Motivated by recent researches in magnetic curves and their flows in different types of geometric manifolds and physical spacetime structures, we compute Lorentz force equations associated with the magnetic b-lines in the binormal direction. Evolution equations of magnetic b-lines due to inextensible Heisenberg antiferromagnetic flow are computed to construct the soliton surface associated with the inextensible Heisenberg antiferromagnetic flow. Then, their explicit solutions are investigated in terms of magnetic and geometric quantities via the conformable fractional derivative method. By considering arc-length and time-dependent orthogonal curvilinear coordinates, we finally determine the necessary and sufficient conditions that have to be satisfied by these quantities to define the Lorentz magnetic flux surfaces based on the inextensible Heisenberg antiferromagnetic flow model.