Rigorous Numerical Approach to Isolation in Dynamical Systems on the Example of the Kuramoto-Sivashinsky Equation

This paper describes a method of rigorous verification of an isolating neighborhood based on computer assisted computations. As an application we study the Kuramoto-Sivashinsky equation. The result of the computer assisted proof was directly used in [9] to prove the existence of heteroclinic solutions of the Kuramoto-Sivashinsky equation.