The Boussinesq equation on the half-line
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913810404605952 |
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| author | Charlier, Christophe |
| author_facet | Charlier, Christophe |
| contents | We study the initial-boundary value problem for the Boussinesq equation on the half-line. Assuming that the solution exists, we prove that it can be recovered from its initial-boundary values via the solution of a $3\times 3$ Riemann-Hilbert problem. The contour consists of $18$ arcs on the unit circle, $18$ segments and $18$ half-lines, and the associated jump matrices involve $9$ reflection coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19663 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Boussinesq equation on the half-line Charlier, Christophe Analysis of PDEs We study the initial-boundary value problem for the Boussinesq equation on the half-line. Assuming that the solution exists, we prove that it can be recovered from its initial-boundary values via the solution of a $3\times 3$ Riemann-Hilbert problem. The contour consists of $18$ arcs on the unit circle, $18$ segments and $18$ half-lines, and the associated jump matrices involve $9$ reflection coefficients. |
| title | The Boussinesq equation on the half-line |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.19663 |