Chasing solitons

Every once in a while, I dive into a topic in science for no reason other than that I find it interesting. This is how I learnt about Titan, laser-cooling, and random walks. This post is about the fourth topic in this series: solitons.

A soliton is a stable wave that maintains its shape and characteristics as it moves around. In 1834, a civil engineer named John Scott Russell spotted a single wave moving through the Edinburgh and Glasgow Union Canal in Scotland. He described it thus in a report to the British Association for the Advancement of Science in 1844 (pp. 319-320):

I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat suddenly stopped—not so the mass of water in the channel which it had put in motion; it accumulated round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued its course along the channel apparently without change of form or diminution of speed. I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles an hour [14 km/h], preserving its original figure some thirty feet [9 m] long and a foot to a foot and a half [30−45 cm] in height. Its height gradually diminished, and after a chase of one or two miles [2–3 km] I lost it in the windings of the channel.

Such, in the month of August 1834, was my first chance interview with that singular and beautiful phenomenon which I have called the Wave of Translation, a name which it now very generally bears; which I have since found to be an important element in almost every case of fluid resistance, and ascertained to be the type of that great moving elevation in the sea, which, with the regularity of a planet, ascends our rivers and rolls along our shores.

Russell was able to reproduce a similar wave in a water tank and study its properties. American physicists later called this wave a 'soliton' because of its solitary nature as well as to recall the name of particles like protons and electrons (to which waves are related by particle-wave duality).

Solitons are unusual in many ways. They are very stable, for one: Russell was able to follow his soliton for almost 3 km before it vanished completely. Solitons are able to collide with each other and still come away intact. There are types of solitons with still more peculiar properties.

These entities are not easy to find: they arise due to the confluence of unusual circumstances. For example, Russell's "wave of translation" was born when a boat moving in a canal suddenly stopped, pushing a single wave of in front that kept going. The top speed at which a wave can move on the surface of a water body is limited by the depth of the body. This is why a tsunami generated in the middle of the ocean can travel rapidly towards the shore, but as it gets closer and the water becomes shallower, it slows down. (Since it must also conserve energy, the kinetic energy it must shed goes into increasing its amplitude, so the tsunami becomes enormous when it strikes land.)

In fluid dynamics, the ratio of the speed of a vessel to the square root of the depth of the water it is moving in is called the Froude number. If the vessel was moving at the maximum speed of a wave in the Union Canal, the Froude number would have been 1.

If the Froude number had been 0.7, the vessel would have generated V-shaped pairs of waves about its prow, reminiscent of the common sight of a ship cutting through water.

Then the vessel started to speed up and its Froude number approached 1. This would have caused the waves generated off the sides to bend away from the prow and straighten at the front. This is the genesis of a soliton. Since the Union Canal has a fixed width, waves forming at the front of the vessel will have had fewer opportunities to dissipate and thus keep moving forward.

Since the boat stopped, it produced the single soliton that won Russell's attention. If it had kept moving, it would have produced a series of solitons in the water, and at the same have acquired a gentle up and down oscillating motion of its own as the Froude number exceeded 1.

Waves occur in a wide variety of contexts in the real world — and in the right conditions, scientists expect to find solitons in almost all of them. For example they have been spotted in optical fibres that carry light waves, in materials carrying a moving wave of magnetisation, and in water currents at the bottom of the ocean.