Solitons are solitary waves that are stable to perturbations.  This talk will focus on the paper "Korteweg--deVries Equation and Generalizations. VI. Methods for Exact Solution" by Gardner, Greene, Kruskal, and Miura which explores solving the Korteweg--deVries equation using inverse scattering, a method pioneered in this paper.  This allows one to write explicit solutions to the KdV equation, including solutions that demonstrate solitons.