Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line II
<|reference_start|>Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line II: We present a new algorithm for the rigorous integration of the variational equation (i.e. producing $\mathcal C^1$ estimates) for a class of dissipative PDEs on the torus. As an application for some parameter value for the Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions we prove the existence of infinite number of homo- and heteroclinic orbits to two periodic orbits. The proof is computer assisted.<|reference_end|>
@article{wilczak2024symbolic,
    title={Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line II},
    author={Daniel Wilczak and Piotr Zgliczy'nski},
    journal={arXiv preprint arXiv:2405.17087},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.17087},
    primaryClass={math.DS cs.NA math.AP math.NA}
}