Solitary wave solutions and sensitivity analysis to the space-time β-fractional Pochhammer–Chree equation in elastic medium
Abstract Solitary wave solutions to the nonlinear evolution equations have recently attracted widespread interest in engineering and physical sciences. In this work, we investigate the fractional generalised nonlinear Pochhammer–Chree equation under the power-law of nonlinearity with order m. This e...
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Nature Portfolio
2024-11-01
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| Online Access: | https://doi.org/10.1038/s41598-024-79102-x |
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| author | Jan Muhammad Usman Younas Ejaz Hussain Qasim Ali Mirwais Sediqmal Krzysztof Kedzia Ahmed Zubair Jan |
| author_facet | Jan Muhammad Usman Younas Ejaz Hussain Qasim Ali Mirwais Sediqmal Krzysztof Kedzia Ahmed Zubair Jan |
| author_sort | Jan Muhammad |
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| description | Abstract Solitary wave solutions to the nonlinear evolution equations have recently attracted widespread interest in engineering and physical sciences. In this work, we investigate the fractional generalised nonlinear Pochhammer–Chree equation under the power-law of nonlinearity with order m. This equation is used to describe longitudinal deformation wave propagation in an elastic rod. In this study, we have secured a variety of exact solitary wave solutions by the assistance of the recently developed technique known as modified generalized exponential rational function method. Exact solutions of various categories, such as bright-dark, bright, mixed, singular, dark, complex, and combined solitons, are extracted. The applied approach is highly efficient and has a significant computational capability to efficiently tackle the solutions with a high degree of accuracy in nonlinear systems. To analyze the governing system, the equation under investigation is converted to an ordinary differential equation through the application of a suitable wave transformation with a $$\beta$$ -derivative. In addition to illustrate the behavior of the solution at various parameter values, we generate 2D and 3D graphs that incorporate pertinent parameters. Moreover, the Galilean transformation is employed to investigate the sensitivity analysis. This research’s results have the potential to enhance comprehension of the nonlinear dynamic characteristics displayed by the defined system and to verify the efficacy of the strategies that have been implemented. The results obtained are a substantial contribution to the comprehension of nonlinear science and nonlinear wave fields that are associated with higher dimensions. |
| format | Article |
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| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Nature Portfolio |
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| spelling | doaj-art-f93d7745c2aa4edbade9653c0692a50f2024-11-24T12:21:45ZengNature PortfolioScientific Reports2045-23222024-11-0114111310.1038/s41598-024-79102-xSolitary wave solutions and sensitivity analysis to the space-time β-fractional Pochhammer–Chree equation in elastic mediumJan Muhammad0Usman Younas1Ejaz Hussain2Qasim Ali3Mirwais Sediqmal4Krzysztof Kedzia5Ahmed Zubair Jan6Department of Mathematics, Shanghai UniversityDepartment of Mathematics, Shanghai UniversityDepartment of Mathematics, University of the PunjabDepartment of Mathematics, University of the ChakwalFaculty of Civil Engineering, Laghman UniversityDepartament of Mechanical Engineering, Wrocław University of Science and TechnologyDepartament of Mechanical Engineering, Wrocław University of Science and TechnologyAbstract Solitary wave solutions to the nonlinear evolution equations have recently attracted widespread interest in engineering and physical sciences. In this work, we investigate the fractional generalised nonlinear Pochhammer–Chree equation under the power-law of nonlinearity with order m. This equation is used to describe longitudinal deformation wave propagation in an elastic rod. In this study, we have secured a variety of exact solitary wave solutions by the assistance of the recently developed technique known as modified generalized exponential rational function method. Exact solutions of various categories, such as bright-dark, bright, mixed, singular, dark, complex, and combined solitons, are extracted. The applied approach is highly efficient and has a significant computational capability to efficiently tackle the solutions with a high degree of accuracy in nonlinear systems. To analyze the governing system, the equation under investigation is converted to an ordinary differential equation through the application of a suitable wave transformation with a $$\beta$$ -derivative. In addition to illustrate the behavior of the solution at various parameter values, we generate 2D and 3D graphs that incorporate pertinent parameters. Moreover, the Galilean transformation is employed to investigate the sensitivity analysis. This research’s results have the potential to enhance comprehension of the nonlinear dynamic characteristics displayed by the defined system and to verify the efficacy of the strategies that have been implemented. The results obtained are a substantial contribution to the comprehension of nonlinear science and nonlinear wave fields that are associated with higher dimensions.https://doi.org/10.1038/s41598-024-79102-xModified generalized exponential rational function methodSolitonsGeneralised nonlinear Pochhammer–Chree equation$$\beta$$ -fractional derivativePower-law nonlinearity |
| spellingShingle | Jan Muhammad Usman Younas Ejaz Hussain Qasim Ali Mirwais Sediqmal Krzysztof Kedzia Ahmed Zubair Jan Solitary wave solutions and sensitivity analysis to the space-time β-fractional Pochhammer–Chree equation in elastic medium Scientific Reports Modified generalized exponential rational function method Solitons Generalised nonlinear Pochhammer–Chree equation $$\beta$$ -fractional derivative Power-law nonlinearity |
| title | Solitary wave solutions and sensitivity analysis to the space-time β-fractional Pochhammer–Chree equation in elastic medium |
| title_full | Solitary wave solutions and sensitivity analysis to the space-time β-fractional Pochhammer–Chree equation in elastic medium |
| title_fullStr | Solitary wave solutions and sensitivity analysis to the space-time β-fractional Pochhammer–Chree equation in elastic medium |
| title_full_unstemmed | Solitary wave solutions and sensitivity analysis to the space-time β-fractional Pochhammer–Chree equation in elastic medium |
| title_short | Solitary wave solutions and sensitivity analysis to the space-time β-fractional Pochhammer–Chree equation in elastic medium |
| title_sort | solitary wave solutions and sensitivity analysis to the space time β fractional pochhammer chree equation in elastic medium |
| topic | Modified generalized exponential rational function method Solitons Generalised nonlinear Pochhammer–Chree equation $$\beta$$ -fractional derivative Power-law nonlinearity |
| url | https://doi.org/10.1038/s41598-024-79102-x |
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