Lie symmetry analysis of (2+1)-dimensional time fractional Kadomtsev-Petviashvili equation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913489945100288 |
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| author | Yu, Jicheng Feng, Yuqiang |
| author_facet | Yu, Jicheng Feng, Yuqiang |
| contents | In this paper, Lie symmetry analysis method is applied to the (2+1)-dimensional time fractional Kadomtsev-Petviashvili (KP) equation with the mixed derivative of Riemann-Liouville time-fractional derivative and integer-order $x$-derivative. We obtained all the Lie symmetries admitted by the KP equation and used them to reduce the (2+1)-dimensional fractional partial differential equation with Riemann-Liouville fractional derivative to some (1+1)-dimensional fractional partial differential equations with Erdélyi-Kober fractional derivative or Riemann-Liouville fractional derivative, thereby getting some exact solutions of the reduced equations. In addition, the new conservation theorem and the generalization of Noether operators are developed to construct the conservation laws for the equation studied. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_09826 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lie symmetry analysis of (2+1)-dimensional time fractional Kadomtsev-Petviashvili equation Yu, Jicheng Feng, Yuqiang Exactly Solvable and Integrable Systems Numerical Analysis Mathematical Physics Analysis of PDEs In this paper, Lie symmetry analysis method is applied to the (2+1)-dimensional time fractional Kadomtsev-Petviashvili (KP) equation with the mixed derivative of Riemann-Liouville time-fractional derivative and integer-order $x$-derivative. We obtained all the Lie symmetries admitted by the KP equation and used them to reduce the (2+1)-dimensional fractional partial differential equation with Riemann-Liouville fractional derivative to some (1+1)-dimensional fractional partial differential equations with Erdélyi-Kober fractional derivative or Riemann-Liouville fractional derivative, thereby getting some exact solutions of the reduced equations. In addition, the new conservation theorem and the generalization of Noether operators are developed to construct the conservation laws for the equation studied. |
| title | Lie symmetry analysis of (2+1)-dimensional time fractional Kadomtsev-Petviashvili equation |
| topic | Exactly Solvable and Integrable Systems Numerical Analysis Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2405.09826 |