English

Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line II

Dynamical Systems 2025-03-25 v2 Numerical Analysis Analysis of PDEs Numerical Analysis

Abstract

We prove the existence of infinite number of homoclinic and heteroclinic orbits to two periodic orbits for the Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions and for some fixed parameter value of the system. The proof is computer assisted and it is based on a new algorithm for rigorous integration of the variational equation for a class of dissipative PDEs on the torus.

Keywords

Cite

@article{arxiv.2405.17087,
  title  = {Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line II},
  author = {Daniel Wilczak and Piotr Zgliczyński},
  journal= {arXiv preprint arXiv:2405.17087},
  year   = {2025}
}

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43 pages