Existence of multi-solitons with any parameters for the 5D energy critical wave equation
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914108162441216 |
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| author | Martel, Yvan Merle, Frank |
| author_facet | Martel, Yvan Merle, Frank |
| contents | For the focusing, energy critical wave equation in dimension 5, we construct multi-solitons with any number of solitons, any choice of signs, speeds, scaling parameters and translation parameters. This requires to revisit in depth previous constructions of multi-solitons based on a unidirectional approach, to fully take into account the dimension of the space and the possibility for solitons to move in any direction.
Then, as a consequence of this more general construction and of the arguments developed in a previous article, the inelastic nature of any collision of solitons is proved under a non-cancellation assumption on the parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19609 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence of multi-solitons with any parameters for the 5D energy critical wave equation Martel, Yvan Merle, Frank Analysis of PDEs For the focusing, energy critical wave equation in dimension 5, we construct multi-solitons with any number of solitons, any choice of signs, speeds, scaling parameters and translation parameters. This requires to revisit in depth previous constructions of multi-solitons based on a unidirectional approach, to fully take into account the dimension of the space and the possibility for solitons to move in any direction. Then, as a consequence of this more general construction and of the arguments developed in a previous article, the inelastic nature of any collision of solitons is proved under a non-cancellation assumption on the parameters. |
| title | Existence of multi-solitons with any parameters for the 5D energy critical wave equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.19609 |