A soliton is a stable isolated (i.e., solitary) traveling nonlinear wave solution to a set of equations that obeys a superposition-like principle (i.e., solitons passing through one another emerge unmodified). Solitons were named by Zabusky and Kruskal, and first appeared in the solution of the Korteweg-de Vries equation.

Korteweg-de Vries equation | Lax pair | sine-Gordon equation