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)1898910.22363/2312-9735-2018-26-3-244-251Research ArticleSimple Model of Nonlinear Spin Waves in Graphene StructuresKulyabovD SAssociate Professor, Doctor of Sciences in Physics and Mathematics, Associate Professor of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University)kulyabov_ds@rudn.universityLovetskiyK PAssociate Professor, Candidate of Sciences in Physics and Mathematics, Associate Professor of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University)lovetskiy_kp@rudn.universityLeAnh NhatPhD student of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University)leanhnhat@tuyenquang.edu.vnPeoples’ Friendship University of Russia (RUDN University)Laboratory of Information Technologies Joint Institute for Nuclear Research1512201826324425104082018Copyright © 2018, Kulyabov D.S., Lovetskiy K.P., Le A.N.2018A series of theoretical and experimental works is known which investigated the magnetic properties of graphene structures. This is due, among other things, to the prospects of using graphene as a material for the needs of the future nanoelectronics and spintronics. In particular, it is known about the presence of ferromagnetic properties at temperatures up to 200 C and above in a single-layer graphene films that are free from impurities. Previously there was proposed a quantum field theoretical model describing the possible mechanism of ferromagnetism in graphene as a result of spontaneous breaking of spin symmetry of the surface density of valence electrons. The possible spatial configurations of the localized spin density were described. In this paper we investigate such spatially localized nonlinear spin configurations of the valence electron density on the graphene surface such as kinks, and their interactions, as well as quasibound metastable states of the interacting kinks and antikinks, that are breathers. The spectrum of such breathers is investigated. It is shown that under certain conditions, this spectrum has a discrete sector, which, in turn, allows us to speak about the possibility of coherent quantum generation of spin waves in graphene structures, which is important in terms of practical applications in nanoelectronics and spintronics.graphenesolitonskinksbreathersnonlinear modelsграфенсолитоныкинкибризерынелинейные модели[Wallace P. R. The Band Theory of Graphite // Physical Review. — 1947. — Vol. 71. — Pp. 622–634.][Kolesnikov D. V., Osipov V. A. The Continuum Gauge Field-Theory Model for Low-Energy Electronic States of Icosahedral Fullerenes // European Physical Journal B. — 2006. — Vol. 49. — P. 465.][Two-Dimensional Gas of Massless Dirac Fermions in Graphene / K. S. Novoselov, A. K. Geim, S. V. Morozov et al. // Nature. — 2005. — Vol. 438. — Pp. 197–200. — DOI: 10.1038/nature04233.][Peres N. M. R. Electronic Properties of Disordered Two-Dimensional Carbon // Physical Review B. — 2006. — Vol. 73. — P. 12541. — DOI: 10.1103/PhysRevB.73.125411.][Room-Temperature Ferromagnetism of Graphene / Y. Wang, Y. Huang, Y. Song et al. // Nano Lett. — 2009. — Vol. 9. — Pp. 220—224.][Electronic Spin Transport and Spin Precession in Single Graphene Layers at Room Temperature / N. Tombros, C. Jozsa, M. Popinciuc et al. // Nature. — 2007. — Vol. 448. — Pp. 571–574.][Ферромагнетизм в графеновых и фуллереновых наноструктурах. Теория, моделирование, эксперимент / Д. Д. Грачёв, Ю. П. Рыбаков, С. Л. А., Ш. Е. Ф. // Вестник Российского университета дружбы народов. Серия: Математика. Информатика. Физика. — 2010. — № 1. — С. 22–27.][Grachev D. D., Sevastyanov L. A. The Quantum Field Model of the Ferromagnetism in Graphene Films // Nanostructures, Mathematical Physics and Modelling. — 2011. — Vol. 4. — Pp. 5–15.][Brauner T. Spontaneous Symmetry Breaking and Nambu–Goldstone Bosons in Quantum Many-Body Systems // Symmetry. — 2010. — Vol. 2. — Pp. 609–657. — DOI: 10.3390/sym2020609.][Watanabe H., Murayama H. Unified Description of Non-Relativistic Nambu–Goldstone Bosons // Physical Review Letters. — 2012. — Vol. 108. — P. 25160.]