soliton

A soliton is a non-linear object which moves through space without dispersion at constant 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 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 $c$, and it can also be shown that the two functions $f$ and $g$ can collide without altering shape. Solitons also occur in non-linear optics and as solutions to field equations in quantum field theory.

Title	soliton
Canonical name	Soliton
Date of creation	2013-03-22 17:47:50
Last modified on	2013-03-22 17:47:50
Owner	invisiblerhino (19637)
Last modified by	invisiblerhino (19637)
Numerical id	10
Author	invisiblerhino (19637)
Entry type	Definition
Classification	msc 35Q51
Classification	msc 37K40
Synonym	solitary wave