Symmetry Analysis and Wave Solutions of Time Fractional Kupershmidt Equation
This study employs the Lie symmetry technique to explore the symmetry features of the time fractional Kupershmidt equation. Specifically, we use the Lie symmetry technique to derive the symmetry generators for this equation, which incorporates a conformal fractional derivative. We use the symmetry g...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/3653687 |
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| _version_ | 1849306485011513344 |
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| author | Shalu Saini Rajeev Kumar Kamal Kumar |
| author_facet | Shalu Saini Rajeev Kumar Kamal Kumar |
| author_sort | Shalu Saini |
| collection | DOAJ |
| description | This study employs the Lie symmetry technique to explore the symmetry features of the time fractional Kupershmidt equation. Specifically, we use the Lie symmetry technique to derive the symmetry generators for this equation, which incorporates a conformal fractional derivative. We use the symmetry generators to transform the fractional partial differential equation into a fractional ordinary differential equation, thereby simplifying the analysis. The obtained reduced equation is of fourth order nonlinear ordinary differential equation. To find the wave solutions, F/G-expansion process has been used to obatin different types of solutions of the time-fractional Kuperschmidt equation. The obtained wave solutions are hyperbolic and trigonometric in nature. We then use Maple software to visually depict these wave solutions for specific parameter values, providing insights into the behaviour of the system under investigation. Peak and kink wave solutions are achieved for the given problem. |
| format | Article |
| id | doaj-art-323dadd8f2fe4a0d93bb93d236973984 |
| institution | Kabale University |
| issn | 1687-0042 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-323dadd8f2fe4a0d93bb93d2369739842025-08-20T03:55:03ZengWileyJournal of Applied Mathematics1687-00422024-01-01202410.1155/2024/3653687Symmetry Analysis and Wave Solutions of Time Fractional Kupershmidt EquationShalu Saini0Rajeev Kumar1Kamal Kumar2Department of MathematicsDepartment of MathematicsDepartment of MathematicsThis study employs the Lie symmetry technique to explore the symmetry features of the time fractional Kupershmidt equation. Specifically, we use the Lie symmetry technique to derive the symmetry generators for this equation, which incorporates a conformal fractional derivative. We use the symmetry generators to transform the fractional partial differential equation into a fractional ordinary differential equation, thereby simplifying the analysis. The obtained reduced equation is of fourth order nonlinear ordinary differential equation. To find the wave solutions, F/G-expansion process has been used to obatin different types of solutions of the time-fractional Kuperschmidt equation. The obtained wave solutions are hyperbolic and trigonometric in nature. We then use Maple software to visually depict these wave solutions for specific parameter values, providing insights into the behaviour of the system under investigation. Peak and kink wave solutions are achieved for the given problem.http://dx.doi.org/10.1155/2024/3653687 |
| spellingShingle | Shalu Saini Rajeev Kumar Kamal Kumar Symmetry Analysis and Wave Solutions of Time Fractional Kupershmidt Equation Journal of Applied Mathematics |
| title | Symmetry Analysis and Wave Solutions of Time Fractional Kupershmidt Equation |
| title_full | Symmetry Analysis and Wave Solutions of Time Fractional Kupershmidt Equation |
| title_fullStr | Symmetry Analysis and Wave Solutions of Time Fractional Kupershmidt Equation |
| title_full_unstemmed | Symmetry Analysis and Wave Solutions of Time Fractional Kupershmidt Equation |
| title_short | Symmetry Analysis and Wave Solutions of Time Fractional Kupershmidt Equation |
| title_sort | symmetry analysis and wave solutions of time fractional kupershmidt equation |
| url | http://dx.doi.org/10.1155/2024/3653687 |
| work_keys_str_mv | AT shalusaini symmetryanalysisandwavesolutionsoftimefractionalkupershmidtequation AT rajeevkumar symmetryanalysisandwavesolutionsoftimefractionalkupershmidtequation AT kamalkumar symmetryanalysisandwavesolutionsoftimefractionalkupershmidtequation |