New fractional Heisenberg antiferromagnetic model and solitonic magnetic flux surfaces with normal direction

2021 ◽  
pp. 2150136
Author(s):  
T. Korpinar ◽  
R. Cem Demirkol ◽  
Z. Korpinar
Keyword(s):  
Magnetic Flux ◽  
Evolution Equations ◽  
Flow Model ◽  
Normal Direction ◽  
Explicit Solutions ◽  
Conformable Fractional Derivative ◽  
Derivative Method ◽  
Schrödinger System ◽  
Antiferromagnetic Model ◽  
Soliton Surface

In this paper, we study applications of fractional Heisenberg antiferromagnetic model associated with the magnetic [Formula: see text]-lines in the normal direction. Evolution equations of magnetic [Formula: see text]-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 examined in terms of magnetic and geometric quantities via the conformable fractional derivative method. Finally, we obtain new numerical fractional solutions for nonlinear fractional Schrödinger system with the inextensible Heisenberg antiferromagnetic flow model.

Explicit, periodic and dispersive soliton solutions to the conformable time-fractional Wu–Zhang system

2021 ◽  
pp. 2150417
Author(s):  
Kalim U. Tariq ◽  
Mostafa M. A. Khater ◽  
Muhammad Younis
Keyword(s):  
Fractional Derivative ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Nonlinear Evolution Equations ◽  
Conformable Fractional Derivative ◽  
Physical Behavior ◽  
Wave Solutions

In this paper, some new traveling wave solutions to the conformable time-fractional Wu–Zhang system are constructed with the help of the extended Fan sub-equation method. The conformable fractional derivative is employed to transform the fractional form of the system into ordinary differential system with an integer order. Some distinct types of figures are sketched to illustrate the physical behavior of the obtained solutions. The power and effective of the used method is shown and its ability for applying different forms of nonlinear evolution equations is also verified.

scholarly journals Exact solutions of the cubic Boussinesq and the coupled Higgs system

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 333-342
Author(s):  
Mahmoud Abdelrahman ◽  
Hanan Alkhidhr ◽  
Dumitru Baleanu ◽  
Mustafa Inc
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Test Problems ◽  
Explicit Solutions ◽  
Computational Results ◽  
Special Test ◽  
Elementary Functions ◽  
The Unified Method ◽  
Unified Method

We present explicit exact solutions of some evolution equations including cubic Boussinesq and coupled Higgs system by the unified method. The explicit solutions are expressed in terms of some elementary functions including trigonometric, exponential, and polynomial. The method is applied to a number of special test problems to test the strength of the method and computational results indicate the power and efficiency of the method.

scholarly journals Vortices in Vacuumless Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
M. A. Marques
Keyword(s):  
Magnetic Flux ◽  
Electromagnetic Fields ◽  
Vacuum State ◽  
Topological Invariant ◽  
Explicit Solutions ◽  
First Order ◽  
Vortex Solutions ◽  
Chern Simons

We investigate the presence of vortex solutions in potentials without vacuum state. The study is conducted considering Maxwell and Chern-Simons dynamics. Also, we use a first-order formalism that helps us to find the solutions and their respective electromagnetic fields and energy densities. As a bonus, we get to calculate the energy without knowing the explicit solutions. Even though the solutions present a large “tail” which goes far away from the origin, the magnetic flux remains a well defined topological invariant.

Lie symmetry analysis and dynamical structures of soliton solutions for the (2 + 1)-dimensional modified CBS equation

2020 ◽  
Vol 34 (25) ◽  
pp. 2050221
Author(s):  
S. Kumar ◽  
D. Kumar
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Surface Condition ◽  
Dynamical Behavior ◽  
Lie Symmetry ◽  
Nonlinear Evolution Equations ◽  
Optimal System ◽  
Explicit Solutions ◽  
Nonlinear Odes ◽  
Symmetry Reductions

In this present article, the new [Formula: see text]-dimensional modified Calogero-Bogoyavlenskii-Schiff (mCBS) equation is studied. Using the Lie group of transformation method, all of the vector fields, commutation table, invariant surface condition, Lie symmetry reductions, infinitesimal generators and explicit solutions are constructed. As we all know, an optimal system contains constructively important information about the various types of exact solutions and it also offers clear understandings into the exact solutions and its features. The symmetry reductions of [Formula: see text]-dimensional mCBS equation is derived from an optimal system of one-dimensional subalgebra of the Lie invariance algebra. Then, the mCBS equation can further be reduced into a number of nonlinear ODEs. The generated explicit solutions have different wave structures of solitons and they are analyzed graphically and physically in order to exhibit their dynamical behavior through 3D, 2D-shapes and respective contour plots. All the produced solutions are definitely new and totally different from the earlier study of the Manukure and Zhou (Int. J. Mod. Phys. B 33, (2019)). Some of these solutions are demonstrated by the means of solitary wave profiles like traveling wave, multi-solitons, doubly solitons, parabolic waves and singular soliton. The calculations show that this Lie symmetry method is highly powerful, productive and useful to study analytically other nonlinear evolution equations in acoustics physics, plasma physics, fluid dynamics, mathematical biology, mathematical physics and many other related fields of physical sciences.

Binormal schrodinger system of Heisenberg ferromagnetic equation in the normal direction with Q-HATM approach

2021 ◽  
pp. 2150082
Author(s):  
Talat Korpinar ◽  
Ridvan Cem Demirkol ◽  
Zeliha Korpinar
Keyword(s):  
Wave Propagation ◽  
Normal Direction ◽  
Fractional Systems ◽  
Magnetic Interpretation ◽  
Normal Orientation ◽  
Homotopy Analysis ◽  
Fractional System ◽  
Parallel Transportation ◽  
The Relationship ◽  
Schrödinger System

In this paper, we first study the applications of the wave propagation flow in the normal direction, which is assumed to be the path of the propagated light radiated by Heisenberg ferromagnetic equation. Then the Coriolis phase is mainly used to demonstrate the relationship between the geometric magnetic phase and parallel transportation of the wave propagation field of the evolving light radiating in the normal orientation with Heisenberg ferromagnetic equation. Moreover, we investigate the geometric magnetic interpretation of the binormal evolution of the wave propagation field in the normal direction by considering the nonlinear fractional system with the repulsive type. Finally, we obtain numerical fractional solutions for the nonlinear fractional systems with the repulsive type by using the [Formula: see text]-Homotopy analysis transform ([Formula: see text]-HATM) method.

scholarly journals Derivative Method Based Orientation Detection of Substation Grounding Grid

Energies ◽  
2018 ◽  
Vol 11 (7) ◽  
pp. 1873 ◽  
Author(s):  
Aamir Qamar ◽  
Muhammad Umair ◽  
Fan Yang ◽  
Muhammad Uzair ◽  
Zeeshan Kaleem
Keyword(s):  
Magnetic Flux ◽  
Flux Density ◽  
Critical Parameters ◽  
Magnetic Flux Density ◽  
Main Peak ◽  
Diagonal Branch ◽  
Grounding Grid ◽  
Derivative Method ◽  
Grounding Grids ◽  
Orientation Detection

The grounding grid is a key part of substation protection, which provides safety to personnel and equipment under normal as well as fault conditions. Currently, the topology of a grounding grid is determined by assuming that its orientation is parallel to the plane of earth. However, in practical scenarios, the assumed orientation may not coincide with the actual orientation of the grounding grid. Hence, currently employed methods for topology detection fails to produce the desired results. Therefore, accurate detection of grounding grid orientation is mandatory for measuring its topology accurately. In this paper, we propose a derivative method for orientation detection of grounding grid in high voltage substations. The proposed method is applicable to both equally and unequally spaced grounding grids. Furthermore, our method can also determine the orientation of grounding grid in the challenging case when a diagonal branch is present in the mesh. The proposed method is based on the fact that the distribution of magnetic flux density is perpendicular to the surface of the earth when a current is injected into the grid through a vertical conductor. Taking the third order derivative of the magnetic flux density, the main peak coinciding with the position of underground conductor is accurately obtained. Thus, the main peak describes the orientation of buried conductor of grounding grid. Simulations are performed using Comsol Multiphysics 5.0 to demonstrate the accuracy of the proposed method. Our results demonstrate that the proposed method calculate the orientation of grounding grid with high accuracy. We also investigate the effect of varying critical parameters of our method.

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