maisМоделирование и анализ информационных системModeling and Analysis of Information Systems1818-10152313-5417Yaroslavl State University10.18255/1818-1015-2014-5-49-60mais-84Research ArticleОригинальные статьиArticlesДвояко-периодические мероморфные решения автономных нелинейных дифференциальных уравненийDoubly Periodic Meromorphic Solutions of Autonomous Nonlinear Differential EquationsКудряшовНиколай АлексеевичDeminaM. V.

доктор физико-математических наук, профессор, заведующий кафедрой прикладной математики, 115409 Россия, г. Москва, Каширское шоссе, 31

доктор физико-математических наук, профессор, заведующий кафедрой прикладной математики; Kashirskoe shosse, 31, Moscow, 115409, Russia

nakudr@gmail.comДеминаМария ВладимировнаKudryashovN. A.

кандидат физико-математических наук, доцент кафедры прикладной математики, 115409 Россия, г. Москва, Каширское шоссе, 31

кандидат физико-математических наук, доцент кафедры прикладной математики; Kashirskoe shosse, 31, Moscow, 115409, Russia

mvdemina@mephi.ruНациональный Исследовательский Ядерный Университет «МИФИ»РоссияNational Research Nuclear University MEPhIRussian Federation2014201020142154960Copyright © Кудряшов Н.А., Демина М.В., 20142014Кудряшов Н.А., Демина М.В.Demina M.V., Kudryashov N.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.mais-journal.ru/jour/article/view/84

Рассматривается задача построения и классификации эллиптических решений нелинейных дифференциальных уравнений. Описывается эффективный метод, позволяющий находить любое эллиптическое решение автономного нелинейного обыкновенного дифференциального уравнения. Метод не требует интегрирования дополнительных дифференциальных уравнений. Большое внимание уделяется методике построения эллиптических решений с несколькими полюсами в параллелограмме периодов. С помощью данного метода найден явный вид всех эллиптических решений до четвертого порядка включительно для обыкновенного дифференциального уравнения, имеющего ряд физических приложений. Рассматриваемый метод допускает естественное обобщение на случай систем обыкновенных дифференциальных уравнений.

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The authors declare that there are no conflicts of interest present.