The history of the soliton

It is pointed out that the discovery of the soliton, its remarkable properties, and the incredible richness of structure involved in its mathematical description occurred in two stages and over a period of almost 140 years. The first reported incident related to the phenomenon of the soliton involves the 'Wave of Translation' described by Scott Russell (1844). Another important development occurred in connection with questions concerning the reason for the finite heat conductivity of solids. These questions led to the conduction of a numerical study by Fermi et al. (1955). The results of this study, called the Fermi-Pasta-Ulam (FPU) experiment, were the motivation for investigations in which the soliton was discovered. This discovery was announced by Zabusky and Kruskal (1965). Attention is also given to the conservation laws and the Miura transformation, the inverse scattering transform, the Lax equation, developments in nonlinear optics, soliton factories, and the need for a unifying point of view.