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}
}
Comments
43 pages