The authors apply the well known Wahlquist-Estabrook prolongation technique to the Kuramoto-Sivashinsky equation. The prolongation algebra turns out to be trivial in the sense that it is commutative. This supports nonintegrability of the equation.
Nijs, H., & Martini, R. (1989). Triviality of the prolongation algebra of the Kuramoto-Sivashinsky equation. Journal of physics A: mathematical and general, 22(18), L861. https://doi.org/10.1088/0305-4470/22/18/001