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<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="research-article" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">Discrete and Continuous Models and Applied Computational Science</journal-id><journal-title-group><journal-title xml:lang="en">Discrete and Continuous Models and Applied Computational Science</journal-title><trans-title-group xml:lang="ru"><trans-title>Discrete and Continuous Models and Applied Computational Science</trans-title></trans-title-group></journal-title-group><issn publication-format="print">2658-4670</issn><issn publication-format="electronic">2658-7149</issn><publisher><publisher-name xml:lang="en">Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">18989</article-id><article-id pub-id-type="doi">10.22363/2312-9735-2018-26-3-244-251</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Modeling and Simulation</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Математическое моделирование</subject></subj-group><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title xml:lang="en">Simple Model of Nonlinear Spin Waves in Graphene Structures</article-title><trans-title-group xml:lang="ru"><trans-title>Простейшая модель нелинейных спиновых волн в графеновых структурах</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Kulyabov</surname><given-names>D S</given-names></name><name xml:lang="ru"><surname>Кулябов</surname><given-names>Дмитрий Сергеевич</given-names></name></name-alternatives><bio xml:lang="en">Associate 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)</bio><bio xml:lang="ru"><p>доцент, доктор физико-математических наук, доцент кафедры прикладной информатики и теории вероятностей РУДН</p></bio><email>kulyabov_ds@rudn.university</email><xref ref-type="aff" rid="aff1"/><xref ref-type="aff" rid="aff2"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Lovetskiy</surname><given-names>K P</given-names></name><name xml:lang="ru"><surname>Ловецкий</surname><given-names>Константин Петрович</given-names></name></name-alternatives><bio xml:lang="en">Associate 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)</bio><bio xml:lang="ru"><p>доцент, кандидат физико-математических наук, доцент кафедры прикладной информатики и теории вероятностей РУДН</p></bio><email>lovetskiy_kp@rudn.university</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Le</surname><given-names>Anh Nhat</given-names></name><name xml:lang="ru"><surname>Ле</surname><given-names>Ань Ньат</given-names></name></name-alternatives><bio xml:lang="en">PhD student of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University)</bio><bio xml:lang="ru"><p>аспирант кафедры прикладной информатики и теории вероятностей РУДН</p></bio><email>leanhnhat@tuyenquang.edu.vn</email><xref ref-type="aff" rid="aff1"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">Peoples’ Friendship University of Russia (RUDN University)</institution></aff><aff><institution xml:lang="ru">Российский университет дружбы народов</institution></aff></aff-alternatives><aff-alternatives id="aff2"><aff><institution xml:lang="en">Laboratory of Information Technologies Joint Institute for Nuclear Research</institution></aff><aff><institution xml:lang="ru">Лаборатория информационных технологий Объединённый институт ядерных исследований</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2018-12-15" publication-format="electronic"><day>15</day><month>12</month><year>2018</year></pub-date><volume>26</volume><issue>3</issue><issue-title xml:lang="en">VOL 26, NO3 (2018)</issue-title><issue-title xml:lang="ru">ТОМ 26, №3 (2018)</issue-title><fpage>244</fpage><lpage>251</lpage><history><date date-type="received" iso-8601-date="2018-08-04"><day>04</day><month>08</month><year>2018</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2018, Kulyabov D.S., Lovetskiy K.P., Le A.N.</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2018, Кулябов Д.С., Ловецкий К.П., Ле А.Н.</copyright-statement><copyright-year>2018</copyright-year><copyright-holder xml:lang="en">Kulyabov D.S., Lovetskiy K.P., Le A.N.</copyright-holder><copyright-holder xml:lang="ru">Кулябов Д.С., Ловецкий К.П., Ле А.Н.</copyright-holder><ali:free_to_read xmlns:ali="http://www.niso.org/schemas/ali/1.0/"/><license><ali:license_ref xmlns:ali="http://www.niso.org/schemas/ali/1.0/">https://creativecommons.org/licenses/by-nc/4.0</ali:license_ref></license></permissions><self-uri xlink:href="https://journals.rudn.ru/miph/article/view/18989">https://journals.rudn.ru/miph/article/view/18989</self-uri><abstract xml:lang="en">A 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.</abstract><trans-abstract xml:lang="ru"><p>Известен ряд экспериментальных и теоретических работ, в которых исследовались магнитные свойства графеновых структур. Это вызвано перспективами использования графена в качестве материала для нужд будущей наноэлектроники и спинтроники. В частности, известно о наличии ферромагнитных свойств при температурах до 200в€-C и выше в однослойных плёнках графена, свободных от примесей. Ранее была предложена модель квантового поля, описывающая возможный механизм ферромагнетизма в графене в результате спонтанного нарушения спиновой симметрии поверхностной плотности валентных электронов. Описаны возможные пространственные конфигурации локализованной спиновой плотности. В этой работе исследуются пространственно локализованные нелинейные спиновые конфигурации плотности валентных электронов на поверхности графена, такие как кинки, их взаимодействие, а также метастабильные состояния взаимодействующих кинков и антикинков, являющихся бризерами. Исследован спектр бризеров. Показано, что при определённых условиях этот спектр имеет дискретный сектор, что, в свою очередь, позволяет говорить о возможности когерентной квантовой генерации спиновых волн в графеновых структурах, что важно с точки зрения практического применения в наноэлектронике и спинтронике.</p></trans-abstract><kwd-group xml:lang="en"><kwd>graphene</kwd><kwd>solitons</kwd><kwd>kinks</kwd><kwd>breathers</kwd><kwd>nonlinear models</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>графен</kwd><kwd>солитоны</kwd><kwd>кинки</kwd><kwd>бризеры</kwd><kwd>нелинейные модели</kwd></kwd-group><funding-group/></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><citation-alternatives><mixed-citation xml:lang="en">P. R. Wallace, The Band Theory of Graphite, Physical Review 71 (1947) 622-634.</mixed-citation><mixed-citation xml:lang="ru">Wallace P. R. 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