Complex structure of time-periodic solutions decoded in Poincaré-Lindstedt series
- Author(s)
- Filip Ficek, Maciej Maliborski
- Abstract
This work explores the rich structure of spherically symmetric time-periodic solutions of the cubic conformal wave equation on $\mathbb{S}^{3}$. We discover that the families of solutions bifurcating from the eigenmodes of the linearised equation form patterns similar to the ones observed for the cubic wave equation. Alongside the Galerkin approaches, we study them using the new method based on the Pad\'{e} approximants. To do so, we provide a rigorous perturbative construction of solutions. Due to the conformal symmetry, the solutions presented in this work serve as examples of large time-periodic solutions of the conformally coupled scalar field on the anti-de Sitter background.
- Organisation(s)
- Gravitational Physics, Department of Mathematics
- Journal
- Physica D: Nonlinear Phenomena
- Volume
- 481
- ISSN
- 0167-2789
- DOI
- https://doi.org/10.1016/j.physd.2025.134864
- Publication date
- 08-2025
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 103019 Mathematical physics, 101002 Analysis, 103028 Theory of relativity
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/964f90e8-36f0-4a35-a48d-9ddaa3a45f7c