In this paper, we firstly obtain the evolution equations of the magnetic field and electric field vectors of polarized light ray propagating along a coiled optical fiber in Minkowski space. Then we define new kinds of binormal motions and new kinds of Hasimoto transformations to relate these evolution equations into the nonlinear Schrodinger’s equation. During this procedure, we use a parallel adapted frame or more commonly known as Bishop frame to characterize the coiled optical fiber geometrically. We also propose perturbed solutions of the nonlinear Schrodinger’s evolution equation that governs the propagation of solitons through the electric field (E) and magnetic field (M) vectors. Finally, we provide some numerical simulations to supplement the analytical outcomes.

Soliton propagation of electromagnetic field vectors of polarized light ray traveling in a coiled optical fiber in Minkowski space with Bishop equations

In this paper, we relate the evolution equations of the electric field and magnetic field vectors of the polarized light ray traveling in a coiled optical fiber in the ordinary space into the nonli...

Soliton propagation of electromagnetic field vectors of polarized light ray traveling in a coiled optical fiber in the ordinary space

Polarization of propagated light with optical solitons along the fiber in de-sitter space S12

In this paper, we investigate the Hasimoto surfaces in Minkowski 3-space. We discussed the geometric properties of Hasimoto surfaces in $\mathbb {M}^{3}$
 for three cases. The Gaussian and mean curvature of Hasimoto surface are found for each case. Then, we give the characterization of parameter curves of Hasimoto surfaces in $\mathbb {M}^{3}.$

Geometry of Hasimoto Surfaces in Minkowski 3-Space

In the present paper, we investigate differential geometric properties the soliton surface M associated with the Betchow-Da Rios Equation. Then, we give derivative formulas of Frenet frame of unit speed curve Φ=Φ(s,t) for all t. Also, we discuss the linear map of Weingarten type in the tangent space of the surface that generates two invariants: k and h. Moreover, we obtain the necessary and sufficient conditions for the soliton surface associated with the Betchow-Da Rios Equation to be minimal surfaces. Finally, we examine an soliton surface associated with the Betchow-Da Rios Equation as an application.

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Differential Geometric Approach of Betchow-Da Rios Soliton Equation

In this paper, we present a unified geometric interpretation of the second AKNS-hierarchies via the geometric concept of Schrodinger flows in the category of symplectic manifolds and binormal motion for curves in the Minkowski 3-space.

Qing Ding

Papers

Schrödinger flows, binormal motion for curves and the second AKNS-hierarchies