Concentric-ring patterns of higher-order lumps in the Kadomtsev--Petviashvili I equation
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913586175016960 |
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| author | Yang, Bo Yang, Jianke |
| author_facet | Yang, Bo Yang, Jianke |
| contents | Large-time patterns of general higher-order lump solutions in the KP-I equation are investigated. It is shown that when the index vector of the general lump solution is a sequence of consecutive odd integers starting from one, the large-time pattern in the spatial $(x, y)$ plane generically would comprise fundamental lumps uniformly distributed on concentric rings. For other index vectors, the large-time pattern would comprise fundamental lumps in the outer region as described analytically by the nonzero-root structure of the associated Wronskian-Hermit polynomial, together with possible fundamental lumps in the inner region that are uniformly distributed on concentric rings generically. Leading-order predictions of fundamental lumps in these solution patterns are also derived. The predicted patterns at large times are compared to true solutions, and good agreement is observed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17364 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Concentric-ring patterns of higher-order lumps in the Kadomtsev--Petviashvili I equation Yang, Bo Yang, Jianke Exactly Solvable and Integrable Systems Pattern Formation and Solitons Large-time patterns of general higher-order lump solutions in the KP-I equation are investigated. It is shown that when the index vector of the general lump solution is a sequence of consecutive odd integers starting from one, the large-time pattern in the spatial $(x, y)$ plane generically would comprise fundamental lumps uniformly distributed on concentric rings. For other index vectors, the large-time pattern would comprise fundamental lumps in the outer region as described analytically by the nonzero-root structure of the associated Wronskian-Hermit polynomial, together with possible fundamental lumps in the inner region that are uniformly distributed on concentric rings generically. Leading-order predictions of fundamental lumps in these solution patterns are also derived. The predicted patterns at large times are compared to true solutions, and good agreement is observed. |
| title | Concentric-ring patterns of higher-order lumps in the Kadomtsev--Petviashvili I equation |
| topic | Exactly Solvable and Integrable Systems Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2411.17364 |