Soliton Waves with the (3+1)-Dimensional Kadomtsev–Petviashvili–Boussinesq Equation in Water Wave Dynamics
We examined the (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq (KP-B) equation, which arises not only in fluid dynamics, superfluids, physics, and plasma physics but also in the construction of connections between the hydrodynamic and optical model fields. Moreover, unlike the Kadomtsev–Petvias...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/1/165 |
| _version_ | 1797436853081604096 |
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| author | Muslum Ozisik Aydin Secer Mustafa Bayram |
| author_facet | Muslum Ozisik Aydin Secer Mustafa Bayram |
| author_sort | Muslum Ozisik |
| collection | DOAJ |
| description | We examined the (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq (KP-B) equation, which arises not only in fluid dynamics, superfluids, physics, and plasma physics but also in the construction of connections between the hydrodynamic and optical model fields. Moreover, unlike the Kadomtsev–Petviashvili equation (KPE), the KP-B equation allows the modeling of waves traveling in both directions and does not require the zero-mass assumption, which is necessary for many scientific applications. Considering these properties enables researchers to obtain more precise results in many physics and engineering applications, especially in research on the dynamics of water waves. We used the modified extended tanh function method (METFM) and Kudryashov’s method, which are easily applicable, do not require further mathematical manipulations, and give effective results to investigate the physical properties of the KP-B equation and its soliton solutions. As the output of the work, we obtained some new singular soliton solutions to the governed equation and simulated them with 3D and 2D graphs for the reader to understand clearly. These results and graphs describe the single and singular soliton properties of the (3+1)-dimensional KP-B equation that have not been studied and presented in the literature before, and the methods can also help in obtaining the solution to the evolution equations and understanding wave propagation in water wave dynamics. |
| first_indexed | 2024-03-09T11:08:34Z |
| format | Article |
| id | doaj.art-e5b142b2bfde4b849a1584069cf2bdd6 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T11:08:34Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-e5b142b2bfde4b849a1584069cf2bdd62023-12-01T00:52:52ZengMDPI AGSymmetry2073-89942023-01-0115116510.3390/sym15010165Soliton Waves with the (3+1)-Dimensional Kadomtsev–Petviashvili–Boussinesq Equation in Water Wave DynamicsMuslum Ozisik0Aydin Secer1Mustafa Bayram2Department of Mathematical Engineering, Yildiz Technical University, Istanbul 34349, TurkeyDepartment of Computer Engineering, Biruni University, Istanbul 34010, TurkeyDepartment of Computer Engineering, Biruni University, Istanbul 34010, TurkeyWe examined the (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq (KP-B) equation, which arises not only in fluid dynamics, superfluids, physics, and plasma physics but also in the construction of connections between the hydrodynamic and optical model fields. Moreover, unlike the Kadomtsev–Petviashvili equation (KPE), the KP-B equation allows the modeling of waves traveling in both directions and does not require the zero-mass assumption, which is necessary for many scientific applications. Considering these properties enables researchers to obtain more precise results in many physics and engineering applications, especially in research on the dynamics of water waves. We used the modified extended tanh function method (METFM) and Kudryashov’s method, which are easily applicable, do not require further mathematical manipulations, and give effective results to investigate the physical properties of the KP-B equation and its soliton solutions. As the output of the work, we obtained some new singular soliton solutions to the governed equation and simulated them with 3D and 2D graphs for the reader to understand clearly. These results and graphs describe the single and singular soliton properties of the (3+1)-dimensional KP-B equation that have not been studied and presented in the literature before, and the methods can also help in obtaining the solution to the evolution equations and understanding wave propagation in water wave dynamics.https://www.mdpi.com/2073-8994/15/1/165Kadomtsev–Petviashvili–Boussinesq equationKudryashov methodmodified extended tanh functionsoliton solution |
| spellingShingle | Muslum Ozisik Aydin Secer Mustafa Bayram Soliton Waves with the (3+1)-Dimensional Kadomtsev–Petviashvili–Boussinesq Equation in Water Wave Dynamics Symmetry Kadomtsev–Petviashvili–Boussinesq equation Kudryashov method modified extended tanh function soliton solution |
| title | Soliton Waves with the (3+1)-Dimensional Kadomtsev–Petviashvili–Boussinesq Equation in Water Wave Dynamics |
| title_full | Soliton Waves with the (3+1)-Dimensional Kadomtsev–Petviashvili–Boussinesq Equation in Water Wave Dynamics |
| title_fullStr | Soliton Waves with the (3+1)-Dimensional Kadomtsev–Petviashvili–Boussinesq Equation in Water Wave Dynamics |
| title_full_unstemmed | Soliton Waves with the (3+1)-Dimensional Kadomtsev–Petviashvili–Boussinesq Equation in Water Wave Dynamics |
| title_short | Soliton Waves with the (3+1)-Dimensional Kadomtsev–Petviashvili–Boussinesq Equation in Water Wave Dynamics |
| title_sort | soliton waves with the 3 1 dimensional kadomtsev petviashvili boussinesq equation in water wave dynamics |
| topic | Kadomtsev–Petviashvili–Boussinesq equation Kudryashov method modified extended tanh function soliton solution |
| url | https://www.mdpi.com/2073-8994/15/1/165 |
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