chebЧебышевский сборникChebyshevskii Sbornik2226-8383Tula State Lev Tolstoy Pedagogical University10.22405/2226-8383-2024-25-2-169-180cheb-1737Research ArticleСтатьиArticleТеория рассеяния для нагруженного уравнения Кортевега—де Фриза отрицательного порядкаScattering theory for the loaded negative order Korteweg–de Vries equationУразбоевГайрат УразалиевичUrazboevGayrat Urazaliyevich

доктор физико-математических наук

doctor of physical and mathematical sciences

gayrat71@mail.ruБалтаеваИрода ИсмаиловнаBaltaevaIroda Ismailovna

кандидат физико-математических наук

candidate of physical and mathematical sciences

iroda-b@mail.ruИсмоиловОхунджон Бахром оглыIsmailovOxunjon Bakhrom uglibakhromboyevich.oxunjon@gmail.comУргенчский государственный университет; Институт математики им. В.И. Романовского Академии наук Республики Узбекистан (Хорезмский филиал)УзбекистанUrgench State University; V. I. Romanovsky Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan (Khorezm Branch)UzbekistanУргенчский государственный университетУзбекистанUrgench State UniversityUzbekistanИнститут математики им. В.И. Романовского Академии наук Республики Узбекистан (Хорезмский филиал)УзбекистанV. I. Romanovsky Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan (Khorezm Branch)Uzbekistan202419072024252169180Copyright © Уразбоев Г.У., Балтаева И.И., Исмоилов О.Б., 20242024Уразбоев Г.У., Балтаева И.И., Исмоилов О.Б.Urazboev G.U., Baltaeva I.I., Ismailov O.B.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.chebsbornik.ru/jour/article/view/1737

В данной работе мы рассматриваем нагруженное уравнение Кортевега–де Фриза отрицательного порядка. Определена эволюция спектральных данных оператора Штурма–Лиувилля с потенциалом, связанным с решением нагруженного уравнения Кортевега–де Фриза отрицательного порядка. Полученные результаты позволяют применить метод обратной задачи для решения нагруженного уравнения Кортевега–де Фриза отрицательного порядка в классе быстро убывающих функций. Приведен пример иллюстрирующий полученные результаты с графиками.

In this paper, we consider the loaded negative order Korteweg–de Vries equation. The evolution of the spectral data of the Sturm–Liouville operator with a potential associated with the solution of the loaded negative order Korteweg–de Vries equation is determined. The obtained results make it possible to apply the inverse problem method to solve the loadednegative order Korteweg–de Vries equation in the class of rapidly decreasing functions. An example of the given problem is given with graphs of the solution.

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