Lie symmetry analysis, particular solutions and conservation laws of a (2+1)-dimensional KdV4 equation
In this paper, a (2+1)-dimensional KdV4 equation is considered. We obtain Lie symmetries of this equation by utilizing Lie point symmetry analysis method, then use them to perform symmetry reductions. By using translation symmetries, two fourth-order ordinary differential equations are obtained. Sol...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2023532?viewType=HTML |
| _version_ | 1797809889195589632 |
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| author | Sixing Tao |
| author_facet | Sixing Tao |
| author_sort | Sixing Tao |
| collection | DOAJ |
| description | In this paper, a (2+1)-dimensional KdV4 equation is considered. We obtain Lie symmetries of this equation by utilizing Lie point symmetry analysis method, then use them to perform symmetry reductions. By using translation symmetries, two fourth-order ordinary differential equations are obtained. Solutions of one fourth order ordinary differential equation are presented by using direct integration method and $ (G'/G) $-expansion method respectively. Furthermore, the corresponding solutions are depicted with appropriate graphical representations. The other fourth-order ordinary differential equation is solved by using power series technique. Finally, two kinds of conserved vectors of this equation are presented by invoking the multiplier method and Noether's theorem respectively. |
| first_indexed | 2024-03-13T06:59:43Z |
| format | Article |
| id | doaj.art-040402904da04f2ab4e7bc760e5c8b17 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-03-13T06:59:43Z |
| publishDate | 2023-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-040402904da04f2ab4e7bc760e5c8b172023-06-07T01:15:56ZengAIMS PressMathematical Biosciences and Engineering1551-00182023-05-01207119781199710.3934/mbe.2023532Lie symmetry analysis, particular solutions and conservation laws of a (2+1)-dimensional KdV4 equationSixing Tao0School of Mathematics and Statistics, Shangqiu Normal University, Shangqiu 476000, ChinaIn this paper, a (2+1)-dimensional KdV4 equation is considered. We obtain Lie symmetries of this equation by utilizing Lie point symmetry analysis method, then use them to perform symmetry reductions. By using translation symmetries, two fourth-order ordinary differential equations are obtained. Solutions of one fourth order ordinary differential equation are presented by using direct integration method and $ (G'/G) $-expansion method respectively. Furthermore, the corresponding solutions are depicted with appropriate graphical representations. The other fourth-order ordinary differential equation is solved by using power series technique. Finally, two kinds of conserved vectors of this equation are presented by invoking the multiplier method and Noether's theorem respectively.https://www.aimspress.com/article/doi/10.3934/mbe.2023532?viewType=HTML(2+1)-dimensional kdv4 equationlie symmetry analysisconservation lawsmultiplier methodnoether's theorem |
| spellingShingle | Sixing Tao Lie symmetry analysis, particular solutions and conservation laws of a (2+1)-dimensional KdV4 equation Mathematical Biosciences and Engineering (2+1)-dimensional kdv4 equation lie symmetry analysis conservation laws multiplier method noether's theorem |
| title | Lie symmetry analysis, particular solutions and conservation laws of a (2+1)-dimensional KdV4 equation |
| title_full | Lie symmetry analysis, particular solutions and conservation laws of a (2+1)-dimensional KdV4 equation |
| title_fullStr | Lie symmetry analysis, particular solutions and conservation laws of a (2+1)-dimensional KdV4 equation |
| title_full_unstemmed | Lie symmetry analysis, particular solutions and conservation laws of a (2+1)-dimensional KdV4 equation |
| title_short | Lie symmetry analysis, particular solutions and conservation laws of a (2+1)-dimensional KdV4 equation |
| title_sort | lie symmetry analysis particular solutions and conservation laws of a 2 1 dimensional kdv4 equation |
| topic | (2+1)-dimensional kdv4 equation lie symmetry analysis conservation laws multiplier method noether's theorem |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2023532?viewType=HTML |
| work_keys_str_mv | AT sixingtao liesymmetryanalysisparticularsolutionsandconservationlawsofa21dimensionalkdv4equation |