Approximate solutions for the inextensible Heisenberg antiferromagnetic flow and solitonic magnetic flux surfaces in the normal direction in Minkowski space

Motivated by recent researches in magnetic curves and their flows in different types of geometric manifolds and physical spacetime structures, we compute fractional Lorentz force equations associated with the magnetic n-lines in the normal direction in Minkowski space. Fractional evolution equations...

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Bibliographic Details
Published in:Optik (Stuttgart) 2021-07, Vol.238, p.166403, Article 166403
Main Authors: Körpınar, Talat, Demirkol, Rıdvan Cem, Körpınar, Zeliha
Format: Article
Language:English
Subjects:
Geometric phase
Heisenberg antiferromagnetic flow
Lorentz force
Magnetic field lines
Magnetic flux surface
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Summary:Motivated by recent researches in magnetic curves and their flows in different types of geometric manifolds and physical spacetime structures, we compute fractional Lorentz force equations associated with the magnetic n-lines in the normal direction in Minkowski space. Fractional evolution equations of magnetic n-lines due to inextensible Heisenberg antiferromagnetic flow are computed to construct the soliton surface associated with the inextensible Heisenberg antiferromagnetic flow. Then, their approximate 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 in Minkowski space.
ISSN:0030-4026
1618-1336
DOI:10.1016/j.ijleo.2021.166403