If it sounds like I’m making up words here, let’s start with some definitions: a soliton is a kind of wave which moves without dispersing. When you cannonball into the pool, the ripples you create radiate away from your impact point and decrease in height as they go. A wave travelling down a narrow canal, though, is reflected when it hits the walls, and can’t spread out. This confinement makes the wave behave as a coherent “packet” that propagates down that canal indefinitely, losing energy only to the viscous forces that hold water molecules together. While solitons are interesting by themselves, they’re difficult to observe without a tank specially designed to balance the dispersive and reflective tendencies of a wave. This is where the vortical (i.e. rotating, as in a vortex) aspect becomes important.
If you’ve ever been canoeing or kayaking, you’ve probably seen surface vortices. When you put your paddle into the water and draw it back, fluid rushes in from the sides to fill the void you create. Oftentimes this results in small eddies, whirlpools which persist for a moment as depressions on the surface, until they lose their angular momentum to the water around them. This usually happens within a few seconds, but it’s possible to create a soliton form of this phenomenon, which will rotate stably for an astoundingly long time. The math governing these phenomena is hideously complex (it falls under the field of nonlinear dispersive partial differential equations), but in the same way that you don’t need kinematic calculations to hit a golf ball, you can see it in action without ever touching a pen to paper. Watch what happens when Youtube user Jeffreyscomputer creates a symmetrical pair of these vortices:
That’s all there is to it! By dipping the plate halfway into the water and drawing it forward at just the right speed (this may take some practice), you can balance out the dispersive effects and create a semi-stable topological defect. As in the image at the top of this post, the two counter-spinning whirlpools are bound together by a sort of “string” under the water’s surface. Thanks to this strange feature, the vortex pair can be treated as a single system with a total angular momentum of zero, which allows it to continue spinning without creating energy-sapping turbulence in the water around it. The smooth dimples they create act as a sort of lens, bending sunlight away and casting a shadow on the bottom of the pool, which lets us witness their amazing longevity.
It’s not a perfect analogy, but this example can be a useful tool for understanding the stability of charge-neutral systems. Like a particle annihilating its antiparticle, if two free vortices spinning opposite directions collided, the angular momentum of one would cancel that of the other, the dimples would disappear, and the energy that was contained in them would radiate away as surface waves. But in a bound state, they behave more like a hydrogen atom: the energy in them is never stationary, but the system as a whole can remain at rest.
So if you feel like performing your own particle collision experiments, there’s no need for a bulky proton accelerator; grab a friend and a pair of plates, find an empty swimming pool, and watch a ballet of motion unfold amid the shifting patterns of sunlight on the bottom.