Half-Wave Maps: Explicit Formulas for Rational Functions with Simple Poles
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910722895642624 |
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| author | Ohlmann, Gaspard |
| author_facet | Ohlmann, Gaspard |
| contents | We establish an explicit formula for the Half-Wave maps equation for rational functions with simple poles. The Lax pair provides a description of the evolution of the poles. By considering a half-spin formulation, we use linear algebra to derive a time evolution equation followed by the half-spins, in the moving frame provided by the Lax pair. We then rewrite this formula using a Toeplitz operator and $G$, the adjoint of the operator of multiplication by $x$ on the Hardy space $L_+^2(\mathbb{R})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00910 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Half-Wave Maps: Explicit Formulas for Rational Functions with Simple Poles Ohlmann, Gaspard Analysis of PDEs 35Q58, 35Q51, 35Q53, 42B10 We establish an explicit formula for the Half-Wave maps equation for rational functions with simple poles. The Lax pair provides a description of the evolution of the poles. By considering a half-spin formulation, we use linear algebra to derive a time evolution equation followed by the half-spins, in the moving frame provided by the Lax pair. We then rewrite this formula using a Toeplitz operator and $G$, the adjoint of the operator of multiplication by $x$ on the Hardy space $L_+^2(\mathbb{R})$. |
| title | Half-Wave Maps: Explicit Formulas for Rational Functions with Simple Poles |
| topic | Analysis of PDEs 35Q58, 35Q51, 35Q53, 42B10 |
| url | https://arxiv.org/abs/2412.00910 |