The beginning of soliton physics in often dated back to the month of
August 1834 when John Scott Russell observed the ``great wave of
translation''. He describes what he saw in [1]:

*"I believe I shall best introduce this phenomenon by describing the circumstances of my own first acquaintance with it. I was observing the motion of a boat which was rapidly along a narrow channel by a pair of hoses, 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 dimension 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 foot and 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 a name which it now very generally bears."*

Due to the work of Stokes, Boussinesq, Rayleigh, Korteweg, de Vries, and many others we know that the ``great wave of translation'' is a special form of a surface water wave.

The equation describing the (unidirectional) propagation of waves on the surface of a shallow channel was derived by Korteweg and de Vries in 1895. After performing a Galilean and variety of scaling transformations, the KdV equation can be written in simplified form:

The KdV equation can admits also a Multi-soliton solution.

[1] J. Scott Russell. Report on waves, Fourteenth meeting of the British Association for the Advancement of Science, 1844.