Rogue wave patterns associated with Adler Moser polynomials in the nonlocal nonlinear Schrödinger equation
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913734447857664 |
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| author | Wang, Tingyou Qin, Zhenyun Mu, Gui Zheng, Fuzhuang Qiao, Zhijun |
| author_facet | Wang, Tingyou Qin, Zhenyun Mu, Gui Zheng, Fuzhuang Qiao, Zhijun |
| contents | In this paper, novel rogue wave patterns in the nolocal nonlinear Schrödinger equation (NLS) are investigated by means of asymptotic analysis, including heart-pentagon, oval-trangle, and fan-trangle. It is demonstrated that when multiple free parameters get considerably large, rogue wave patterns can approximately be predicted by the root structures of Adler-Moser polynomials. These polynomials, which extend the Yablonskii-Vorob'ev polynomial hierarchy, exhibit richer geometric shapes in their root distributions. The (x,t)-plane is partitioned into three regions and through a combination of asymptotic results in different regions, unreported rogue wave patterns can be probed. Predicted solutions are compared with true rogue waves in light of graphical illustrations and numerical confirmation, which reveal excellent agreement between them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03757 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rogue wave patterns associated with Adler Moser polynomials in the nonlocal nonlinear Schrödinger equation Wang, Tingyou Qin, Zhenyun Mu, Gui Zheng, Fuzhuang Qiao, Zhijun Pattern Formation and Solitons Exactly Solvable and Integrable Systems In this paper, novel rogue wave patterns in the nolocal nonlinear Schrödinger equation (NLS) are investigated by means of asymptotic analysis, including heart-pentagon, oval-trangle, and fan-trangle. It is demonstrated that when multiple free parameters get considerably large, rogue wave patterns can approximately be predicted by the root structures of Adler-Moser polynomials. These polynomials, which extend the Yablonskii-Vorob'ev polynomial hierarchy, exhibit richer geometric shapes in their root distributions. The (x,t)-plane is partitioned into three regions and through a combination of asymptotic results in different regions, unreported rogue wave patterns can be probed. Predicted solutions are compared with true rogue waves in light of graphical illustrations and numerical confirmation, which reveal excellent agreement between them. |
| title | Rogue wave patterns associated with Adler Moser polynomials in the nonlocal nonlinear Schrödinger equation |
| topic | Pattern Formation and Solitons Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2503.03757 |