Time-periodic solutions to the cubic wave equation: an elementary constructive approach
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915571480657920 |
|---|---|
| author | Ficek, Filip |
| author_facet | Ficek, Filip |
| contents | We present an elementary proof of existence of infinite family of time-periodic solutions to the one-dimensional nonlinear cubic wave equation with Dirichlet boundary conditions. It relies on the first order perturbative expansion and uses the Banach contraction principle to show existence of nearby solutions. In contrast to the previous results, this approach provides us explicit information about the frequencies and structures of the obtained solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20054 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-periodic solutions to the cubic wave equation: an elementary constructive approach Ficek, Filip Analysis of PDEs Mathematical Physics 35B10 We present an elementary proof of existence of infinite family of time-periodic solutions to the one-dimensional nonlinear cubic wave equation with Dirichlet boundary conditions. It relies on the first order perturbative expansion and uses the Banach contraction principle to show existence of nearby solutions. In contrast to the previous results, this approach provides us explicit information about the frequencies and structures of the obtained solutions. |
| title | Time-periodic solutions to the cubic wave equation: an elementary constructive approach |
| topic | Analysis of PDEs Mathematical Physics 35B10 |
| url | https://arxiv.org/abs/2510.20054 |