I remember solitons being a big/cool thing years back. I went poking about and while I can see applications in fiber optics there’s not much else. Well, I’ve likely searched poorly.
Do other fields use them and in what manner?
Many years ago a colleague was doing a PhD on chemical based computers (something of a dead end as it turned out) but he was looking at the ability of materials to propagate a soliton as a physical wave in the chemical backbone.
I have a feeling some surface acoustic wave (SAW) devices use solitons in their operation, but this might be more on the bleeding edge research than commercial devices. Avoiding dispersion in such devices would be expected to significantly improve their bandwidth. But I’m out of by depth going any further.
Bolding mine. Perfectly phrased question. 
I have to admit that I only know of their use in fiber optics, where they actually help in information transmission. It’s actually a nifty way to turn a potential problem (even a tiny amount of dispersion means that your short optical pulse will eventually spread out into a low, long pulse that will overlap its neighbors and get buried in the noise) into a way to do business (use nonlinearity in the fiber optic medium itself to produce self-assembling solitons that fight the spread). I remember Lin F. Molenauer at Bell Labs explaining this effect, which I’d never heard of before.
Of course, like many other effects, this one is something that exists in nature, whether you want it or not, whether it’s beneficial or not. As lecturers have told me, and as the Wikipedia article says, solitons were first discovered as a phenomenon in water waves in the Union Canal in Scotland, back in 1834. Since I heard that, I’ve wondered if solitons are responsible, in some cases at least, for the rogue wave phenomenon I’ve read about in C.S. Forester maritime novels. That would be a case where the effect is something clearly undesirable.
The Wikipedia page gives examples of solitons in other circumstances, but no other uses: Soliton - Wikipedia
Fiber optics is probably the easiest application. You have a long, controlled environment you can tune to to match the various dispersion types the pulse will encounter (or vice versa).
I did think there would be more tangible applications but apparently not. Maybe the investigation of natural solitons will eventually lead to broader practical applications.
Not sure what is being thought of here.
A soliton is a single cycle wave packet. In water examples are tidal waves and bores. Tsunamis are another example. They are a phenomenon common to any wave propagation environment. At least that is the only definition I have ever heard of. Perhaps the OP has some other meaning?
Unless the OP is discussing something besides a wave phenomenon, they are hardly new or recently popular. As I mentioned, they are used in the descriptions of tides-which go back hundreds of years and are hardly novel.
I saw Francis Vaughan’s comment about using solitons in fiber optic communications-a neat way to take advantage of a particular physical phenomenon, but hardly a new discovery in physics.
Perhaps the OP read about some phenomenon that was described using solitons and that was the first time the phenomenon was described that way?
A characteristic property of solitons is that they resist dispersion, and can interact without scattering irreversibly. Yes, they have been recognized since the 1800s and therefore today are not novel, but that does not mean that the study of non-linear differential equations has stopped in the meantime, nor that there cannot be relatively novel applications, such as in optics.
I agree completely. The study of solitons is an active area of research. I did my graduate work studying a form of a soliton and the last project I worked on before retiring involved soliton internal tidal waves.
I was responding to the OP who seemed to think (perhaps I misinterpreted) that solitons were just discovered or put to use in the 90s. We all agree that they have been an important part of wave studies for a very long time.
Solitons in non-linear electrical transmission lines are sometimes used for pulsing of samplers for use in sampling oscilloscopes, vector network analyzers, and other test equipment. As in the case of solitons in fiber optics, you have a carefully-engineered, uniform, nonlinear and dispersive medium.