Answers are grounded in this paper and cite their sources.
We present a new algorithm for the rigorous integration of the variational equation (i.e. producing C¹ 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.
No takes yet. Share an insight, caveat, or question.
Wilczak et al. (2024) studied this question.
Synapse has enriched 8 closely related papers on similar clinical questions. Consider them for comparative context: