A soliton is a single solitary wave with a very high amplitude1, which behaves very differently to normal waves.
Solitons were first discovered back in 1844, by John Scott Russell (1808 - 1882), quite by accident. He had been observing a boat being pulled along a canal, when the boat stopped, and a mass of water built up in front of it. The water then rolled forward, leaving the boat behind, and continued, as a solitary wave of water, 30 feet long and one to one-and-a-half feet high. Russell followed it on horseback for about two miles, and observed that it gradually diminished in size, until finally he lost it.
Russell was convinced that this wave, which he named the 'Wave of Translation' was a very important phenomenon, and studied it in more detail. However, his contemporaries did not agree.
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A soliton is different to a normal wave, because the speed of the wave is related to the size of the wave. For a soliton, the bigger the wave the faster it travels. Contrast this with sound waves: if two sounds are made at the same time you hear them at the same time, you don't hear the louder one first.
If two solitons collide, the larger one takes energy away from the smaller one, leaving the larger travelling faster and the smaller travelling slower.
The mathematics behind solitons is incredibly complicated. It is non-linear mathematics, which means that it is only relatively recently that we have been able to study them in depth, with the advent of computer technology.
Solitons in Nature
Solitons occur in nature. One example of a soliton on a river is the Severn Bore which travels 21 miles from Awre to Gloucester. Another soliton was observed on the M25 motorway after an accident, which caused a tailback. After the accident had been cleared, the cars started to move again, but a wave of cars travelling closer together went backwards round the motorway at a speed of 39mph several times until there were not enough cars to support it.
There are solitons inside of you, too. When you feel something, your nerves send an electrical signal to your brain. If you, for example were to put your hand into hot coals, your nerves would generate a soliton which would travel to your brain much more quickly than a normal wave, hopefully resulting in you removing your hand.
The future of Solitons
Because solitons remain the same size and shape, and don't diminish like normal waves, they may have applications in telecommunications. Now data is transmitted as normal waves, so every so often a repeater needs to be put into the stream to boost data which is getting diminished. This would be unnecessary for solitons.
Particle physicists think that some of the most elementary particles may be made up of solitons.