kaz29Вестник Казахстанско-Британского технического университетаHerald of the Kazakh-British Technical University1998-66882959-8109Казахстанско-Британский Технический Университет10.55452/1998-6688-2026-23-2-26-34kaz29-2875Research ArticleМАТЕМАТИЧЕСКИЕ НАУКИMATHEMATICAL SCIENCESАНАЛИТИЧЕСКИЕ РЕШЕНИЯ (2+1)-МЕРНОГО ОБОБЩЕННОГО УРАВНЕНИЯ БЕНДЖАМИНА-ОНОANALYTICAL SOLUTIONS OF THE (2+1)-DIMENSIONAL GENERALIZED BENJAMIN-ONO EQUATIONhttps://orcid.org/0000-0002-0819-5338ШайховаГ. Н.ShaikhovaG. N.

PhD, ассоциированный профессор.

Астана

PhD, Associate Professor.

Astana

g.shaikhova@gmail.comЕвразийский национальный университет им. Л.Н. ГумилеваКазахстанL.N. Gumilyov Eurasian National UniversityKazakhstan2026270620262322634Copyright © Шайхова Г.Н., 20262026Шайхова Г.Н.Shaikhova G.N.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestnik.kbtu.edu.kz/jour/article/view/2875

(2+1)-мерное обобщенное уравнение Бенджамина-Оно моделирует распространение длинноволновых волн малой амплитуды на поверхности мелкой воды. Построение явных решений (2+1)-мерного обобщенного уравнения Бенджамина-Оно не только обеспечивает теоретическую поддержку экспериментальным исследованиям, но и дает строгую основу для решения прикладных задач, возникающих в нелинейной динамике волн. В данной работе исследовано распространение волн, описываемое (2+1)-мерным обобщенным уравнением Бенджамина-Оно в нелинейных средах с учетом дисперсионных эффектов. Для этого в качестве аналитических инструментов получения явных решений используются метод функций синуса-косинуса и метод гиперболического тангенса. Показано, что эти методы эффективны для широкого класса нелинейных уравнений математической физики. С их помощью получены решения в виде периодических волн и уединенных волн; для графического представления результатов построены трехмерные и двумерные графики при выборе подходящих значений параметров модели.

The (2+1)-dimensional generalized Benjamin-Ono equation models the propagation of small-amplitude, long-wavelength waves on the surface of shallow water. Constructing explicit solutions of the (2+1)-dimensional generalized Benjamin-Ono equation not only provides theoretical support for experimental investigations but also offers a rigorous basis for addressing applied problems arising in nonlinear wave dynamics. In this work, we investigate wave propagation governed by the (2+1)-dimensional generalized Benjamin-Ono equation in nonlinear media, accounting for dispersive effects. To this end, the sine-cosine function method and the hyperbolic tangent method are employed as analytical tools for deriving explicit solutions. The methods prove effective for a broad class of nonlinear equations encountered in mathematical physics. Using these approaches, periodic-wave solutions and solitary wave solutions are obtained, and to illustrate the obtained results, we plot 3D and 2D plots by setting suitable values of the involved parameters.

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