PlanetPhysics/Soliton

A soliton is a non-linear [[../TrivialGroupoid/|object]] which moves through space without dispersion at constant [[../Velocity/|speed]]. They occur naturally as solutions to the Korteweg - de Vries equation. They were first observed by John Scott Russell in the 19th century and then by Martin Kruskal and Norman Zabusky (who coined the term soliton) in a famous [[../ComputerSimulation/|computer simulation]] in 1965. Insight into solitons can be obtained by noting that the Korteweg - de Vries equation satisfies D'Alembert's solution:

$u(x,t)=f(x-ct)+g(x+ct)$

We see at once that this satisfies two important criteria: it has a constant [[../Velocity/|velocity]] $c$, and it can also be shown that the two [[../Bijective/|functions]] $f$ and $g$ can collide without altering shape. Solitons also occur in non-linear optics and as solutions to [[../CosmologicalConstant2/|field]] equations in [[../SpaceTimeQuantizationInQuantumGravityTheories/|quantum field theory]].