New class of time-periodic solutions to the 1D cubic wave equation
Analysis of PDEs
2025-06-13 v1 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.2506.10839,
title = {New class of time-periodic solutions to the 1D cubic wave equation},
author = {Filip Ficek and Maciej Maliborski},
journal= {arXiv preprint arXiv:2506.10839},
year = {2025}
}
Comments
18 pages, 2 figures. Includes Mathematica code and data files