Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)2291810.22363/2658-4670-2019-27-4-365-377Research ArticleNumerical modeling of stationary pseudospin waves on a graphene monoatomic filmsNhậtLê Anh<p>PhD student of Department of Applied Probability and Informatics</p>leanhnhat@tuyenquang.edu.vnLovetskiyKonstantin P.<p>Docent, PhD in Physics and Mathematics, Associate Professor at the Department of Applied Probability and Informatics</p>lovetskiy-kp@rudn.ruSevastianovLeonid A.<p>Professor, Doctor of Sciences in Physics and Mathematics, Professor at the Department of Applied Probability and Informatics</p>sevastianov-la@rudn.ruKulyabovDmitry S.<p>Docent, Doctor of Sciences in Physics and Mathematics, Professor at the Department of Applied Probability and Informatics</p>kulyabov-ds@rudn.ruPeoples’ Friendship University of Russia (RUDN University)Bogoliubov Laboratory of Theoretical Physics Joint Institute for Nuclear ResearchLaboratory of Information Technologies Joint Institute for Nuclear Research1512201927436537719022020Copyright © 2019, Nhật L.A., Lovetskiy K.P., Sevastianov L.A., Kulyabov D.S.2019<p>For the first time, the theoretical model of the spin-electron structure of a singlelayer graphene film was proposed by Wallace. The literature also describes ferromagnetism generated by none of the three common causes: impurities, defects, boundaries. We believe that the source of ferromagnetism is the spontaneous breaking of spin symmetry in a graphene film. The classical field model describing spontaneously broken symmetry is necessarily non-linear. Among non-linear models, the simplest is the well-known 4 model. We believe that, as a first approximation, we can describe with its help all the characteristics of spin waves that interest us, their spectra, and the domain structure of ferromagnetism in graphene. The model admits kink and anti-kink exact solutions and a quasiparticle breather, which we modeled numerically. We use the kink-anti-kink interaction energy obtained numerically to solve the Schrdinger equation, which simulates the quantum dynamics of breathers, which underlies the description of spin waves. 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