The KdV in cosmology: A useful tool or a distraction?

In a recent article by J. Lidsey, an interesting link has been established between the Kortewegde Vries (KdV) equation and the equations describing cosmological inflation. Due to this link, the author was able to devise rather a simple way of construction of inflationary solutions. We here demonstrate that the technique developed therein is but a consequence of a linearizability of the original cosmological equations. Furthermore, we show the required linearized equation to be nothing else but a Schrödinger equation. To emphasize the importance of this fact, we provide the reader with a way to use this relationship for a construction of not just one but an entire family of exact solutions. In conclusion, we discuss the general possibility to involve the KdV equation involvement in cosmological dynamics and provide a particular example where this equation might arise.