A Novel Geometric Realization of the Yajima-Oikawa Equations
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915069036593152 |
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| author | Calini, Annalisa Ivey, Thomas A. |
| author_facet | Calini, Annalisa Ivey, Thomas A. |
| contents | We show that the Yajima-Oikawa (YO) equations, a model of short wave-long wave interaction, arise from a simple geometric flow on curves in the 3-dimensional sphere $S^3$ that are transverse to the standard contact structure. For the family of periodic plane wave solutions of the YO equations studied by Wright, we construct the associated transverse curves, derive their closure condition, and exhibit several examples with non-trivial topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12946 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Novel Geometric Realization of the Yajima-Oikawa Equations Calini, Annalisa Ivey, Thomas A. Differential Geometry Exactly Solvable and Integrable Systems 37K10, 37K25, 53A40, 53E50, We show that the Yajima-Oikawa (YO) equations, a model of short wave-long wave interaction, arise from a simple geometric flow on curves in the 3-dimensional sphere $S^3$ that are transverse to the standard contact structure. For the family of periodic plane wave solutions of the YO equations studied by Wright, we construct the associated transverse curves, derive their closure condition, and exhibit several examples with non-trivial topology. |
| title | A Novel Geometric Realization of the Yajima-Oikawa Equations |
| topic | Differential Geometry Exactly Solvable and Integrable Systems 37K10, 37K25, 53A40, 53E50, |
| url | https://arxiv.org/abs/2412.12946 |