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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2404.17156 |
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| _version_ | 1866929327953674240 |
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| author | Benoudina, Nardjess Khalique, Chaudry Massood Lin, Ji |
| author_facet | Benoudina, Nardjess Khalique, Chaudry Massood Lin, Ji |
| contents | This paper discusses the construction of a new $(3+1)$-dimensional Korteweg-de Vries (KdV) equation. By employing the KdV's recursion operator, we extract two equations, and with elemental computation steps, the obtained result is $ 3u_{xyt}+3u_{xzt}-(u_{t}-6uu_{x}+u_{xxx})_{yz}-2\left(u_{x}\partial_{x}^{-1}u_{y}\right)_{xz}-2\left(u_{x}\partial_{x}^{-1}u_{z}\right)_{xy}=0 $. We then transform the new equation to a simpler one to avoid the appearance of the integral in the equation. Thereafter, we apply the Lie symmetry technique and gain a $7$-dimensional Lie algebra $L_7$ of point symmetries. The one-dimensional optimal system of Lie subalgebras is then computed and used in the reduction process to achieve seven exact solutions. These obtained solutions are graphically illustrated as 3D and 2D plots that show different propagations of solitary wave solutions such as breather, periodic, bell shape, and others. Finally, the conserved vectors are computed by invoking Ibragimov's method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17156 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Construction of a new (3 + 1)-dimensional KdV equation and its closed-form solutions with solitary wave behaviour and conserved vectors Benoudina, Nardjess Khalique, Chaudry Massood Lin, Ji Mathematical Physics Exactly Solvable and Integrable Systems This paper discusses the construction of a new $(3+1)$-dimensional Korteweg-de Vries (KdV) equation. By employing the KdV's recursion operator, we extract two equations, and with elemental computation steps, the obtained result is $ 3u_{xyt}+3u_{xzt}-(u_{t}-6uu_{x}+u_{xxx})_{yz}-2\left(u_{x}\partial_{x}^{-1}u_{y}\right)_{xz}-2\left(u_{x}\partial_{x}^{-1}u_{z}\right)_{xy}=0 $. We then transform the new equation to a simpler one to avoid the appearance of the integral in the equation. Thereafter, we apply the Lie symmetry technique and gain a $7$-dimensional Lie algebra $L_7$ of point symmetries. The one-dimensional optimal system of Lie subalgebras is then computed and used in the reduction process to achieve seven exact solutions. These obtained solutions are graphically illustrated as 3D and 2D plots that show different propagations of solitary wave solutions such as breather, periodic, bell shape, and others. Finally, the conserved vectors are computed by invoking Ibragimov's method. |
| title | Construction of a new (3 + 1)-dimensional KdV equation and its closed-form solutions with solitary wave behaviour and conserved vectors |
| topic | Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2404.17156 |