Can railway tracks support solitons?

A soliton is a wave that can travel through its medium for long distances without dissipation. Usually the different frequencies in a sharply peaked waves will spread out as they move. It is this dispersion that causes the rumble of thunder. However in some special cases the medium might allow all frequencies to travel a the same speed and a wave can travel unaltered for long distances.

I was walking in a the park next to a railway line and I heard a train approach and pass me. The strange thing was that there was no train. I wonder if a train had halted some distance away and a soliton sound wave had propagated down the tracks.

If this is possible it might explain some reports of “ghost trains”. I have raised this question with Herriot Watt university and if they respond I will update this post.