Emergent Mind
Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line II
(2405.17087)
Published May 27, 2024
in
math.DS
,
cs.NA
,
math.AP
,
and
math.NA
Abstract
We present a new algorithm for the rigorous integration of the variational equation (i.e. producing $\mathcal C1$ 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.
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