New class of time-periodic solutions to the 1D cubic 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_ | 1866912426970054656 |
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| author | Ficek, Filip Maliborski, Maciej |
| author_facet | Ficek, Filip Maliborski, Maciej |
| contents | In recent papers (arXiv:2407.16507, arXiv:2408.05158) we presented results suggesting the existence of a new class of time-periodic solutions to the defocusing cubic wave equation on a one-dimensional interval with Dirichlet boundary conditions. Here we confirm these findings by rigorously constructing solutions from this class. The proof uses rational arithmetic computations to verify essential operator bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10839 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New class of time-periodic solutions to the 1D cubic wave equation Ficek, Filip Maliborski, Maciej Analysis of PDEs Mathematical Physics 35B10, 68V05, 35B32, 35L71 In recent papers (arXiv:2407.16507, arXiv:2408.05158) we presented results suggesting the existence of a new class of time-periodic solutions to the defocusing cubic wave equation on a one-dimensional interval with Dirichlet boundary conditions. Here we confirm these findings by rigorously constructing solutions from this class. The proof uses rational arithmetic computations to verify essential operator bounds. |
| title | New class of time-periodic solutions to the 1D cubic wave equation |
| topic | Analysis of PDEs Mathematical Physics 35B10, 68V05, 35B32, 35L71 |
| url | https://arxiv.org/abs/2506.10839 |