PlanetPhysics/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.