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arXiv · 2405.17087

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

Daniel Wilczak·Piotr Zgliczyński
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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.

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Daniel Wilczak, Piotr Zgliczyński. 2024-05-27. Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line II. https://arxiv.org/abs/2405.17087

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