Symbolic dynamics for Kuramoto-Sivashinsky PDE on the line --- a computer-assisted proof
arXiv:1710.003293 citationsh-index: 20
Originality Incremental advance
AI Analysis
For researchers in dynamical systems and PDEs, this work offers a rigorous proof of complex dynamics in a canonical chaotic PDE, though the result is specific to a particular parameter and boundary condition.
The paper provides a computer-assisted proof of symbolic dynamics and a countable infinity of periodic orbits with arbitrarily large periods for the Kuramoto-Sivashinsky PDE on the line with specific boundary conditions and parameter value ν=0.1212.
The Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions and with parameter $ν=0.1212$ is considered. We give a computer-assisted proof the existence of symbolic dynamics and countable infinity of periodic orbits with arbitrary large periods.