Scalar behavior for a complex multi-soliton arising in blow-up for a semilinear 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_ | 1866917195306500096 |
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| author | Azaiez, Asma Jendrej, Jacek Zaag, Hatem |
| author_facet | Azaiez, Asma Jendrej, Jacek Zaag, Hatem |
| contents | This paper deals with blow-up for the complex-valued semilinear wave equation with power nonlinearity in dimension 1. Up to a rotation of the solution in the complex plane, we show that near a characteristic blow-up point, the solution behaves exactly as in the real-valued case. Namely, up to a rotation in the complex plane, the solution decomposes into a sum of a finite number of decoupled solitons with alternate signs. The main novelty of our proof is a resolution of a complex-valued first order Toda system governing the evolution of the positions and the phases of the solitons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04505 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scalar behavior for a complex multi-soliton arising in blow-up for a semilinear wave equation Azaiez, Asma Jendrej, Jacek Zaag, Hatem Analysis of PDEs 35B40, 35B44, 35L05, 35L51, 35L67, 35L71 This paper deals with blow-up for the complex-valued semilinear wave equation with power nonlinearity in dimension 1. Up to a rotation of the solution in the complex plane, we show that near a characteristic blow-up point, the solution behaves exactly as in the real-valued case. Namely, up to a rotation in the complex plane, the solution decomposes into a sum of a finite number of decoupled solitons with alternate signs. The main novelty of our proof is a resolution of a complex-valued first order Toda system governing the evolution of the positions and the phases of the solitons. |
| title | Scalar behavior for a complex multi-soliton arising in blow-up for a semilinear wave equation |
| topic | Analysis of PDEs 35B40, 35B44, 35L05, 35L51, 35L67, 35L71 |
| url | https://arxiv.org/abs/2501.04505 |