matmessМатематические заметки СВФУMathematical notes of NEFU2411-93262587-876XСеверо-Восточный федеральный университет имени М.К. Аммосова10.25587/SVFU.2023.75.56.006matmess-108Research ArticleМАТЕМАТИКАИнтегрирование нагруженного уравнения МКДФ с источником в классе быстроубывающих функцийIntegration of the loaded MKDV equation with a source in the class of rapidly decreasing functionsХоитметовУ. А.HoitmetovU. A.

Хоитметов Умид Азадович

ул. Х. Алимджана, 14, Ургенч 220100, Узбекистан

Umid A. Hoitmetov

14 Kh. Alimdjan Street, Urgench, 220100, Uzbekistan

x_umid@mail.ruСобировШ. К.SobirovSh. Q.

Cобиров Шехзод Кучкарбой угли

ул. Х. Алимджана, 14, Ургенч 220100, Узбекистан

Shekhzod Q. Sobirov

14 Kh. Alimdjan Street, Urgench, 220100, Uzbekistan

shehzod6285@mail.ruУргенчский государственный университет, кафедра прикладной математики и математической физикиУзбекистанUrgench State University, Department of Applied Mathematics and Mathematical PhysicsUzbekistan2023300620233027591Copyright © Хоитметов У.А., Собиров Ш.К., 20232023Хоитметов У.А., Собиров Ш.К.Hoitmetov U.A., Sobirov S.Q.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://matmess.elpub.ru/jour/article/view/108

Рассматривается задача Коши для нагруженного модифицированного уравнения Кортевега — де Фриза с самосогласованным источником. Получена эволюция данных рассеяния оператора Дирака, потенциал которого является решением нагруженного модифицированного уравнения Кортевега — де Фриза с самосогласованным источником в классе быстроубывающих функций. Приведен конкретный пример, иллюстрирующий применение полученных результатов.

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