Do Rogue Wave Exist in the Kadomtesv-Petviashivili I Equation ?
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909110654468096 |
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| author | Zhang, Jie-Fang Zhang, Zhao Zhang, Meng-yang Jin, Mei-zhen |
| author_facet | Zhang, Jie-Fang Zhang, Zhao Zhang, Meng-yang Jin, Mei-zhen |
| contents | There is considerable fundamental theoretical and applicative interest in obtaining two-dimensional rogue wave similar to one-dimensional rogue wave of the nonlinear Schrödinger equation. Here, we first time proposes a self-mapping transformation and analytically predict the existence of a family of novel spatio-temporal rogue wave solutions for the Kadomtesv-Petviashivili equation. We discover that these spatio-temporal rogue waves showing a strong analogy characteristics of the short-lives with rogue waves of the NLS equation. Our fingdings can also provide a solid mathematical basis for theory and application in shallow water, plasma and optics. This technique could be available to construct rogue-like waves of (2+1)-dimensional nonlinear wave models. Also, these studies could be helpful to deepen our understandings and enrich our knowledge about rogue waves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09980 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Do Rogue Wave Exist in the Kadomtesv-Petviashivili I Equation ? Zhang, Jie-Fang Zhang, Zhao Zhang, Meng-yang Jin, Mei-zhen Pattern Formation and Solitons There is considerable fundamental theoretical and applicative interest in obtaining two-dimensional rogue wave similar to one-dimensional rogue wave of the nonlinear Schrödinger equation. Here, we first time proposes a self-mapping transformation and analytically predict the existence of a family of novel spatio-temporal rogue wave solutions for the Kadomtesv-Petviashivili equation. We discover that these spatio-temporal rogue waves showing a strong analogy characteristics of the short-lives with rogue waves of the NLS equation. Our fingdings can also provide a solid mathematical basis for theory and application in shallow water, plasma and optics. This technique could be available to construct rogue-like waves of (2+1)-dimensional nonlinear wave models. Also, these studies could be helpful to deepen our understandings and enrich our knowledge about rogue waves. |
| title | Do Rogue Wave Exist in the Kadomtesv-Petviashivili I Equation ? |
| topic | Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2402.09980 |