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

T. Körpınar, R. Cem Demirkol, Z. Körpinar, V. Asil

Abstract


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.

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DOI: https://doi.org/10.31349/RevMexFis.67.452

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REVISTA MEXICANA DE FÍSICA, year 67, issue 3, May-June 2021. Bimonthly Journal published by Sociedad Mexicana de Física, A. C. Departamento de Física, 2º Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Apartado Postal 70-348. Tel. (+52)55-5622-4946, https://rmf.smf.mx/ojs/rmf, e-mail: rmf@ciencias.unam.mx. Chief Editor: José Alejandro Ayala Mercado. INDAUTOR Certificate of Reserve: 04-2019-080216404400-203, ISSN: 2683-2224 (on line), 0035-001X (print), both granted by Instituto Nacional del Derecho de Autor. Responsible for the last update of this issue, Technical Staff of Sociedad Mexicana de Física, A. C., Fís. Efraín Garrido Román, 2º. Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Date of last modification, May 1st., 2021.

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