A Brief History of Solitons and the KDV Equation

Soliton theory is an interdisciplinary area at the interface of mathematics and physics. It studies a special class of nonlinear partial differential equations (NLPDEs) having solutions that are waves which behave like particles. Amazingly, unlike most NLPDEs, we can write exact formulas for the solutions to these ‘soliton equations’. This article is a review providing the historical context necessary to appreciate these spectacular developments, a brief overview of the early history of the field, and a list of references to consult for additional information.