The issue is many kinds of solutions exist, but aren't common in different fields. On a guitar string, waves are 1d waves in a 1d world. In water everyone knows only standard waves. Which are 1d solitons in a 2d "world". In the electromag field everyone only knows light, which are 2d solitons in a 3d world. Electrons have an axis of rotation that does not point in any spatial or temporal direction.
So everybody thinks these are far more different than they really are.
But the wonder is that water has "light rays", 1d solitons in a 3d world (ie. under water). Dolphins love making them and playing with them. It's possible to make them with your hand in a pool, it's just pretty hard, but with a bit of practice. You need to hold your hand flat above the water, splash down, then retract your hand hard and get out of the way. The faster you retract your hand the further they'll go (but you need time to get out of the way). If you do it right a ring of water bubbles will go into a straight line several meters. Dolphins make them go hundreds of meters, and play with them, seemingly for fun. They aim them at eachother and pass them along (these don't have the same geometric structure as light rays, just the same movement. Except that they trap bubbles and so they "fall upward", especially when they slow down)
Water has "particle-antiparticle soliton pairs". You stick your hand, held flat, 90 degrees to the surface, half submerged, and you move it through the water, parallel to the surface. You do it right, 2 vortices will leave and move through the water. You can see circular shadows move over the bottom of the pool (because of the dimple shape where the vortex meets the surface). These you can probably get to the other side of a quiet pool if you try hard.
According to my math, it should be possible to make a version of this where the vortices rotate around each other. And you should be able to make any even number of vortices (like 4, 6, 8, or 800 for that matter) but I've never done even 2 rotating, nor have I been able to make 4 move together.
Water has 2d solitons in 2d as well, but you can't make just them. If you make 2 waves intersect at exactly 90 degrees, every so often the intersection point will "leave" on it's own. A "hill" on the water will start moving through the water, and you'll swear to God something is moving below the water, but there's nothing there but the wave. But this is almost impossible. You can try in a huge pool (ie. no reflections), and nobody but you in there.
It's weird to think about the properties water has that the electric field does not appear to have. For instance, water has a surface, which reflects solitons. Is there a surface in the electric field somewhere? Would it be a mirror in space, that is not just a perfect reflector of light rays but of matter too?