Soliton

A soliton is a stable isolated (i.e., solitary) traveling nonlinear wave solution to a set of equations that obeys a superposition-like principle (i.e., solitons passing through one another emerge unmodified). Solitons were named by Zabusky and Kruskal, and first appeared in the solution of the Korteweg-de Vries equation, which describes weakly nonlinear shallow water waves.

The discovery of solitons is credited to John Scott Russell (1808-1882), a young Scottish engineer. In his "Report on Waves", he describes observations he made while in a boat on the Union Canal at Hermiston, close to Edinburgh. He wrote

"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, preserving its original figure some thirty feet long and a foot to a foot and a half in height. Its height gradually diminished, and after a chase of one or two miles 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."

Russell believed that this solitary wave (the Wave of Translation) was a fundamentally important observation, but others were unconvinced, and his reputation was based on other achievements. including the "wave line" system of hull construction that revolutionized 19th century naval architecture. However, in the 1960's, when applied scientists began to use computers to study nonlinear wave propagation, Russell's ideas were rediscovered. Russell thought of the solitary wave as a self-sufficient dynamic entity, a "thing" with many of the properties of a particle. Today, it is one element of the complex dynamical behaviour of wave systems.