1. Introduction Zabusky and Kruskal [1965] introduced the concept of a soliton—a spatially localized solution of a nonlinear partial differential equation with the property that this solution always regains its initial shape and velocity after interacting with another localized disturbance. They were led to the concept of a soliton by their careful computational study of solutions of the Korteweg–de Vries (or KdV) equation, (See [Zabusky 2005] for his summary of this history.) After that breakthrough, they and their colleagues found that the KdV equation has many remarkable properties, including the property discovered by Gardner, Greene, Kruskal and Miura [Gardner et al. 1967]: the KdV equation can be solved exactly, as an initial-value problem, starting with arbitrary initial data in a suitable space. This discovery was revolutionary, and it drew the interest of many people. We note especially the work of Zakharov and Faddeev [1971], who showed that the KdV equation is a nontrivial example of an infinite-dimensional Hamiltonian system that is completely integrable. This means that under a canonical change of variables, the original problem can be written in terms of action-angle variables, in which the action variables are constants of the motion, while the angle variables evolve according to nearly trivial ordinary differential equations (ODEs).