On simulations of 3D fractional WBBM model through mathematical and graphical analysis with the assists of fractionality and unrestricted parameters
Abstract This study retrieves some novel exact solutions to the family of 3D space–time fractional Wazwaz–Benjamin–Bona–Mahony (WBBM) equations in the context of diverse nonlinear physical phenomena resulting from water wave mechanics. The family of WBBM equations is transformed for this purpose usi...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-07-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-024-61405-8 |
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| author | Nur Hasan Mahmud Shahen Foyjonnesa Md. Al Amin M. M. Rahman |
| author_facet | Nur Hasan Mahmud Shahen Foyjonnesa Md. Al Amin M. M. Rahman |
| author_sort | Nur Hasan Mahmud Shahen |
| collection | DOAJ |
| description | Abstract This study retrieves some novel exact solutions to the family of 3D space–time fractional Wazwaz–Benjamin–Bona–Mahony (WBBM) equations in the context of diverse nonlinear physical phenomena resulting from water wave mechanics. The family of WBBM equations is transformed for this purpose using a space and time fractional transformation into an ordinary differential equation (ODE). The ODE then uses a strong method, namely the Unified Method. Consequently, lump solutions, dark-bright soliton, singular and multiple soliton solutions, and periodic solutions are investigated. The disparities between the current study's conclusions and previously acquired solutions via other approaches are examined. All wave solutions produced are determined to be novel in terms of fractionality, unrestricted parameters, and implemented technique sense. The impact of unrestricted parameters and fractionality on the obtained solutions are visually presented, along with physical explanations. It is observed that the wave portents are varied with the increase of unrestricted parameters as well as fractionality. We dynamically showed that the appropriate transformation and the applied Unified approach more proficient in the study of water wave dynamics and might be used in future researches to clarify the many physical phenomena. The novelty of this work validate that the proposed method seem simple and useful tools for obtaining the solutions in PDEs and it is expected to use in mathematical physics and optical engineering. |
| format | Article |
| id | doaj-art-cd350da8586944779a56433901aef835 |
| institution | OA Journals |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-cd350da8586944779a56433901aef8352025-08-20T01:56:24ZengNature PortfolioScientific Reports2045-23222024-07-0114111710.1038/s41598-024-61405-8On simulations of 3D fractional WBBM model through mathematical and graphical analysis with the assists of fractionality and unrestricted parametersNur Hasan Mahmud Shahen0Foyjonnesa1Md. Al Amin2M. M. Rahman3Department of Mathematics, Bangladesh University of Engineering and TechnologyDepartment of Mathematics, Bangladesh University of Engineering and TechnologyDepartment of Mathematics, University of RajshahiDepartment of Mathematics, Bangladesh University of Engineering and TechnologyAbstract This study retrieves some novel exact solutions to the family of 3D space–time fractional Wazwaz–Benjamin–Bona–Mahony (WBBM) equations in the context of diverse nonlinear physical phenomena resulting from water wave mechanics. The family of WBBM equations is transformed for this purpose using a space and time fractional transformation into an ordinary differential equation (ODE). The ODE then uses a strong method, namely the Unified Method. Consequently, lump solutions, dark-bright soliton, singular and multiple soliton solutions, and periodic solutions are investigated. The disparities between the current study's conclusions and previously acquired solutions via other approaches are examined. All wave solutions produced are determined to be novel in terms of fractionality, unrestricted parameters, and implemented technique sense. The impact of unrestricted parameters and fractionality on the obtained solutions are visually presented, along with physical explanations. It is observed that the wave portents are varied with the increase of unrestricted parameters as well as fractionality. We dynamically showed that the appropriate transformation and the applied Unified approach more proficient in the study of water wave dynamics and might be used in future researches to clarify the many physical phenomena. The novelty of this work validate that the proposed method seem simple and useful tools for obtaining the solutions in PDEs and it is expected to use in mathematical physics and optical engineering.https://doi.org/10.1038/s41598-024-61405-8The 3D fractional WBBM equation familyThe unified methodWater wave mechanicsMathematical physicsShallow water |
| spellingShingle | Nur Hasan Mahmud Shahen Foyjonnesa Md. Al Amin M. M. Rahman On simulations of 3D fractional WBBM model through mathematical and graphical analysis with the assists of fractionality and unrestricted parameters Scientific Reports The 3D fractional WBBM equation family The unified method Water wave mechanics Mathematical physics Shallow water |
| title | On simulations of 3D fractional WBBM model through mathematical and graphical analysis with the assists of fractionality and unrestricted parameters |
| title_full | On simulations of 3D fractional WBBM model through mathematical and graphical analysis with the assists of fractionality and unrestricted parameters |
| title_fullStr | On simulations of 3D fractional WBBM model through mathematical and graphical analysis with the assists of fractionality and unrestricted parameters |
| title_full_unstemmed | On simulations of 3D fractional WBBM model through mathematical and graphical analysis with the assists of fractionality and unrestricted parameters |
| title_short | On simulations of 3D fractional WBBM model through mathematical and graphical analysis with the assists of fractionality and unrestricted parameters |
| title_sort | on simulations of 3d fractional wbbm model through mathematical and graphical analysis with the assists of fractionality and unrestricted parameters |
| topic | The 3D fractional WBBM equation family The unified method Water wave mechanics Mathematical physics Shallow water |
| url | https://doi.org/10.1038/s41598-024-61405-8 |
| work_keys_str_mv | AT nurhasanmahmudshahen onsimulationsof3dfractionalwbbmmodelthroughmathematicalandgraphicalanalysiswiththeassistsoffractionalityandunrestrictedparameters AT foyjonnesa onsimulationsof3dfractionalwbbmmodelthroughmathematicalandgraphicalanalysiswiththeassistsoffractionalityandunrestrictedparameters AT mdalamin onsimulationsof3dfractionalwbbmmodelthroughmathematicalandgraphicalanalysiswiththeassistsoffractionalityandunrestrictedparameters AT mmrahman onsimulationsof3dfractionalwbbmmodelthroughmathematicalandgraphicalanalysiswiththeassistsoffractionalityandunrestrictedparameters |