Solitonic Analysis of the Newly Introduced Three-Dimensional Nonlinear Dynamical Equations in Fluid Mediums

Mohammed N. Alshehri (), Saad Althobaiti, Ali Althobaiti, Rahmatullah Ibrahim Nuruddeen, Halliru S. Sambo and Abdulrahman F. Aljohani
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Mohammed N. Alshehri: Department of Mathematics, College of Arts and Science, Najran University, P.O. Box 1988, Najran 66468, Saudi Arabia
Saad Althobaiti: Department of Sciences and Technology, Ranyah University College, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Ali Althobaiti: Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Rahmatullah Ibrahim Nuruddeen: Department of Mathematics, Faculty of Physical Sciences, Federal University Dutse, P.O. Box 7156, Dutse 720212, Nigeria
Halliru S. Sambo: Department of Physics, Faculty of Physical Sciences, University of Maiduguri, Maiduguri 600104, Nigeria
Abdulrahman F. Aljohani: Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 47512, Saudi Arabia

Mathematics, 2024, vol. 12, issue 20, 1-23

Abstract: The emergence of higher-dimensional evolution equations in dissimilar scientific arenas has been on the rise recently with a vast concentration in optical fiber communications, shallow water waves, plasma physics, and fluid dynamics. Therefore, the present study deploys certain improved analytical methods to perform a solitonic analysis of the newly introduced three-dimensional nonlinear dynamical equations (all within the current year, 2024), which comprise the new (3 + 1) Kairat-II nonlinear equation, the latest (3 + 1) Kairat-X nonlinear equation, the new (3 + 1) Boussinesq type nonlinear equation, and the new (3 + 1) generalized nonlinear Korteweg–de Vries equation. Certainly, a solitonic analysis, or rather, the admittance of diverse solitonic solutions by these new models of interest, will greatly augment the findings at hand, which mainly deliberate on the satisfaction of the Painleve integrability property and the existence of solitonic structures using the classical Hirota method. Lastly, this study is relevant to contemporary research in many nonlinear scientific fields, like hyper-elasticity, material science, optical fibers, optics, and propagation of waves in nonlinear media, thereby unearthing several concealed features.

Keywords: higher-order evolution equations; Kairat equations; Boussinesq equation; KdV equation; Kudryashov method; solitonic analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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