Periodic solutions for the 1D cubic wave equation with Dirichlet boundary conditions
- Author(s)
- Filip Ficek, Maciej Maliborski
- Abstract
We study time-periodic solutions for the cubic wave equation on an interval with Dirichlet boundary conditions. We begin by following the perturbative construction of Vernov and Khrustalev and provide a rigorous derivation of the fourth-order expansion in small amplitude, which we use to verify the Galerkin scheme. In the main part, we focus on exploring large solutions numerically. We find an intricate bifurcation structure of time-periodic solutions forming a fractal-like pattern and explore it for the first time. Our results suggest that time-periodic solutions exist for arbitrary frequencies, with appearance of fine bifurcation structure likely related to the Cantor set families of solutions described in previous rigorous works.
- Organisation(s)
- Department of Mathematics, Gravitational Physics
- Journal
- Nonlinearity
- Volume
- 38
- No. of pages
- 23
- ISSN
- 0951-7715
- DOI
- https://doi.org/10.48550/arXiv.2407.16507
- Publication date
- 06-2025
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 103019 Mathematical physics
- Keywords
- ASJC Scopus subject areas
- Statistical and Nonlinear Physics, Mathematical Physics, General Physics and Astronomy, Applied Mathematics
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/3d58dff6-dc46-4f1c-a92b-6999fbde1195