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

2024/05/27 by Wilczak, Daniel, Zgliczyński, Piotr
#35B10 #35B30 #35B40 #35B45 #65G40 #65N30 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2405.17087

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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