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arXiv · 2506.10839

New class of time-periodic solutions to the 1D cubic wave equation

Filip Ficek·Maciej Maliborski
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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.

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Filip Ficek, Maciej Maliborski. 2025-06-12. New class of time-periodic solutions to the 1D cubic wave equation. https://arxiv.org/abs/2506.10839

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