Estevez–Mansfield–Clarkson equation: Investigation of Breathers, two waves, and solitary wave solutions in shallow water phenomena and engineering fluid dynamics
This article focuses on investigating the Estevez–Mansfield–Clarkson equation describing the complex dynamics of shallow water waves and the physics of fluids. For such equations, analytical wave solutions are of the utmost importance in numerical and theoretical studies. Firstly, we introduce a tra...
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Elsevier
2025-10-01
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| Series: | Case Studies in Thermal Engineering |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2214157X25009839 |
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| author | U. Younas J. Muhammad T.A. Sulaiman H.F. Ismael Homan Emadifar Wael W. Mohammed Karim K. Ahmed |
| author_facet | U. Younas J. Muhammad T.A. Sulaiman H.F. Ismael Homan Emadifar Wael W. Mohammed Karim K. Ahmed |
| author_sort | U. Younas |
| collection | DOAJ |
| description | This article focuses on investigating the Estevez–Mansfield–Clarkson equation describing the complex dynamics of shallow water waves and the physics of fluids. For such equations, analytical wave solutions are of the utmost importance in numerical and theoretical studies. Firstly, we introduce a traveling wave transformation, and then the recently developed methods known as the modified generalized Riccati equation mapping approach and the modified generalized exponential rational function technique are applied. A variety of soliton solutions, like dark, bright, singular, bright-dark, dark-singular, as well as the hyperbolic, periodic, and exponential solutions, are secured. Secondly, the Hirota method is applied to the studied equation, and we get the bilinear form, and a variety of breathers and two-wave solutions are extracted. Breather waves are solitary waves that demonstrate periodic structure in either space or time, as well as partial localization. In a variety of physical domains, such as ocean engineering, fluid mechanics, optics, hydrodynamics, and quantized superfluidity, breathers have been observed to perform essential functions in nonlinear physics. The variety of graphs in three dimensional with projection and two dimensional with variation of time have been plotted to observe the dynamics of the waves. The outcomes of this work could help to confirm the efficiency of the used techniques and improve understanding of the nonlinear dynamics exhibited by the system at issue. The gained results significantly help to clarify nonlinear science and the nonlinear wave disciplines in higher dimensions. |
| format | Article |
| id | doaj-art-2828ee8e76c94f01862c720d91fd0e5d |
| institution | DOAJ |
| issn | 2214-157X |
| language | English |
| publishDate | 2025-10-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Case Studies in Thermal Engineering |
| spelling | doaj-art-2828ee8e76c94f01862c720d91fd0e5d2025-08-20T02:48:57ZengElsevierCase Studies in Thermal Engineering2214-157X2025-10-017410672310.1016/j.csite.2025.106723Estevez–Mansfield–Clarkson equation: Investigation of Breathers, two waves, and solitary wave solutions in shallow water phenomena and engineering fluid dynamicsU. Younas0J. Muhammad1T.A. Sulaiman2H.F. Ismael3Homan Emadifar4Wael W. Mohammed5Karim K. Ahmed6Department of Mathematics, Shanghai University, No. 99 Shangda Road, Shanghai 200444, ChinaDepartment of Mathematics, Shanghai University, No. 99 Shangda Road, Shanghai 200444, ChinaDepartment of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India; Department of Mathematics, Federal University Dutse, NigeriaDepartment of Mathematics, College of Science, University of Zakho, Zakho, Iraq; Department of Computer Science, College of Science, Knowledge University, Erbil, IraqDepartment of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India; Department of Basic Sciences, Technical and Vocational University (TVU), Tehran, Iran; Corresponding author at: Department of Basic Sciences, Technical and Vocational University (TVU), Tehran, Iran.Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi ArabiaDepartment of Mathematics, Faculty of Engineering, German International University (GIU), New Administrative Capital, Cairo, EgyptThis article focuses on investigating the Estevez–Mansfield–Clarkson equation describing the complex dynamics of shallow water waves and the physics of fluids. For such equations, analytical wave solutions are of the utmost importance in numerical and theoretical studies. Firstly, we introduce a traveling wave transformation, and then the recently developed methods known as the modified generalized Riccati equation mapping approach and the modified generalized exponential rational function technique are applied. A variety of soliton solutions, like dark, bright, singular, bright-dark, dark-singular, as well as the hyperbolic, periodic, and exponential solutions, are secured. Secondly, the Hirota method is applied to the studied equation, and we get the bilinear form, and a variety of breathers and two-wave solutions are extracted. Breather waves are solitary waves that demonstrate periodic structure in either space or time, as well as partial localization. In a variety of physical domains, such as ocean engineering, fluid mechanics, optics, hydrodynamics, and quantized superfluidity, breathers have been observed to perform essential functions in nonlinear physics. The variety of graphs in three dimensional with projection and two dimensional with variation of time have been plotted to observe the dynamics of the waves. The outcomes of this work could help to confirm the efficiency of the used techniques and improve understanding of the nonlinear dynamics exhibited by the system at issue. The gained results significantly help to clarify nonlinear science and the nonlinear wave disciplines in higher dimensions.http://www.sciencedirect.com/science/article/pii/S2214157X25009839SolitonsHirota methodModified generalized Riccati equation mapping techniqueEstevez–Mansfield–Clarkson equationBreather solutionsModified generalized exponential rational function method |
| spellingShingle | U. Younas J. Muhammad T.A. Sulaiman H.F. Ismael Homan Emadifar Wael W. Mohammed Karim K. Ahmed Estevez–Mansfield–Clarkson equation: Investigation of Breathers, two waves, and solitary wave solutions in shallow water phenomena and engineering fluid dynamics Case Studies in Thermal Engineering Solitons Hirota method Modified generalized Riccati equation mapping technique Estevez–Mansfield–Clarkson equation Breather solutions Modified generalized exponential rational function method |
| title | Estevez–Mansfield–Clarkson equation: Investigation of Breathers, two waves, and solitary wave solutions in shallow water phenomena and engineering fluid dynamics |
| title_full | Estevez–Mansfield–Clarkson equation: Investigation of Breathers, two waves, and solitary wave solutions in shallow water phenomena and engineering fluid dynamics |
| title_fullStr | Estevez–Mansfield–Clarkson equation: Investigation of Breathers, two waves, and solitary wave solutions in shallow water phenomena and engineering fluid dynamics |
| title_full_unstemmed | Estevez–Mansfield–Clarkson equation: Investigation of Breathers, two waves, and solitary wave solutions in shallow water phenomena and engineering fluid dynamics |
| title_short | Estevez–Mansfield–Clarkson equation: Investigation of Breathers, two waves, and solitary wave solutions in shallow water phenomena and engineering fluid dynamics |
| title_sort | estevez mansfield clarkson equation investigation of breathers two waves and solitary wave solutions in shallow water phenomena and engineering fluid dynamics |
| topic | Solitons Hirota method Modified generalized Riccati equation mapping technique Estevez–Mansfield–Clarkson equation Breather solutions Modified generalized exponential rational function method |
| url | http://www.sciencedirect.com/science/article/pii/S2214157X25009839 |
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