Soliton

Summary

A soliton is a localised wave that moves at constant speed without changing its shape. It keeps its shape and speed after it collides with other solitons; the only trace of the collision is a shift in position. Solitons arise when nonlinear steepening and dispersion balance, in equations such as the Korteweg–De Vries equation, the nonlinear Schrödinger equation and the sine-Gordon equation. They are central in the theory of integrable equations and in models of water waves and of light pulses in optical fibres.