Lie symmetry analysis, particular solutions and conservation laws for the dissipative (2 + 1)- dimensional AKNS equation
The dissipative (2 + 1)-dimensional AKNS equation is considered in this paper. First, the Lie symmetry analysis method is applied to the dissipative (2 + 1)-dimensional AKNS and six point symmetries are obtained. Symmetry reductions are performed by utilizing these obtained point symmetries and four...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-08-01
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| Series: | Communications in Analysis and Mechanics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/cam.2023024?viewType=HTML |
| _version_ | 1797361215920406528 |
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| author | Sixing Tao |
| author_facet | Sixing Tao |
| author_sort | Sixing Tao |
| collection | DOAJ |
| description | The dissipative (2 + 1)-dimensional AKNS equation is considered in this paper. First, the Lie symmetry analysis method is applied to the dissipative (2 + 1)-dimensional AKNS and six point symmetries are obtained. Symmetry reductions are performed by utilizing these obtained point symmetries and four differential equations are derived, including a fourth-order ordinary differential equation and three partial differential equations. Thereafter, the direct integration approach and the $ (G'/G^{2})- $expansion method are employed to solve the ordinary differential respectively. As a result, a periodic solution in terms of the Weierstrass elliptic function is obtained via the the direct integration approach, while six kinds of including the hyperbolic function types and the hyperbolic function types are derived via the $ (G'/G^{2})- $expansion method. The corresponding graphical representation of the obtained solutions are presented by choosing suitable parametric values. Finally, the multiplier technique and the classical Noether's theorem are employed to derive conserved vectors for the dissipative (2 + 1)-dimensional AKNS respectively. Consequently, eight local conservation laws for the dissipative (2 + 1)-dimensional AKNS equation are presented by utilizing the multiplier technique and five local conservation laws are derived by invoking Noether's theorem. |
| first_indexed | 2024-03-08T15:50:45Z |
| format | Article |
| id | doaj.art-68057aff3e484647b1d2a75c0cf7a715 |
| institution | Directory Open Access Journal |
| issn | 2836-3310 |
| language | English |
| last_indexed | 2024-03-08T15:50:45Z |
| publishDate | 2023-08-01 |
| publisher | AIMS Press |
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| series | Communications in Analysis and Mechanics |
| spelling | doaj.art-68057aff3e484647b1d2a75c0cf7a7152024-01-09T05:54:06ZengAIMS PressCommunications in Analysis and Mechanics2836-33102023-08-0115349451410.3934/cam.2023024Lie symmetry analysis, particular solutions and conservation laws for the dissipative (2 + 1)- dimensional AKNS equationSixing Tao0School of Mathematics and Statistics, Shangqiu Normal University, Shangqiu 476000, ChinaThe dissipative (2 + 1)-dimensional AKNS equation is considered in this paper. First, the Lie symmetry analysis method is applied to the dissipative (2 + 1)-dimensional AKNS and six point symmetries are obtained. Symmetry reductions are performed by utilizing these obtained point symmetries and four differential equations are derived, including a fourth-order ordinary differential equation and three partial differential equations. Thereafter, the direct integration approach and the $ (G'/G^{2})- $expansion method are employed to solve the ordinary differential respectively. As a result, a periodic solution in terms of the Weierstrass elliptic function is obtained via the the direct integration approach, while six kinds of including the hyperbolic function types and the hyperbolic function types are derived via the $ (G'/G^{2})- $expansion method. The corresponding graphical representation of the obtained solutions are presented by choosing suitable parametric values. Finally, the multiplier technique and the classical Noether's theorem are employed to derive conserved vectors for the dissipative (2 + 1)-dimensional AKNS respectively. Consequently, eight local conservation laws for the dissipative (2 + 1)-dimensional AKNS equation are presented by utilizing the multiplier technique and five local conservation laws are derived by invoking Noether's theorem.https://www.aimspress.com/article/doi/10.3934/cam.2023024?viewType=HTMLlie symmetry analysisthe dissipative (2 + 1)-dimensional akns equationconservation lawsthe multiplier techniquenoether's theorem |
| spellingShingle | Sixing Tao Lie symmetry analysis, particular solutions and conservation laws for the dissipative (2 + 1)- dimensional AKNS equation Communications in Analysis and Mechanics lie symmetry analysis the dissipative (2 + 1)-dimensional akns equation conservation laws the multiplier technique noether's theorem |
| title | Lie symmetry analysis, particular solutions and conservation laws for the dissipative (2 + 1)- dimensional AKNS equation |
| title_full | Lie symmetry analysis, particular solutions and conservation laws for the dissipative (2 + 1)- dimensional AKNS equation |
| title_fullStr | Lie symmetry analysis, particular solutions and conservation laws for the dissipative (2 + 1)- dimensional AKNS equation |
| title_full_unstemmed | Lie symmetry analysis, particular solutions and conservation laws for the dissipative (2 + 1)- dimensional AKNS equation |
| title_short | Lie symmetry analysis, particular solutions and conservation laws for the dissipative (2 + 1)- dimensional AKNS equation |
| title_sort | lie symmetry analysis particular solutions and conservation laws for the dissipative 2 1 dimensional akns equation |
| topic | lie symmetry analysis the dissipative (2 + 1)-dimensional akns equation conservation laws the multiplier technique noether's theorem |
| url | https://www.aimspress.com/article/doi/10.3934/cam.2023024?viewType=HTML |
| work_keys_str_mv | AT sixingtao liesymmetryanalysisparticularsolutionsandconservationlawsforthedissipative21dimensionalaknsequation |