On the origin of the Korteweg-de Vries equation

TL;DR

This paper explores the historical development of the Korteweg-de Vries equation, highlighting key differences and connections between Boussinesq's and Korteweg-de Vries's contributions over a sixty-year period.

Contribution

It provides a detailed comparison of Boussinesq's and Korteweg-de Vries's work, clarifying lesser-known differences and connections in the origin of the equation.

Findings

Highlights differences between Boussinesq and Korteweg-de Vries contributions.

Clarifies historical connections in the development of the equation.

Reviews lesser-known aspects of the equation's origin.

Abstract

The Korteweg-de Vries equation has a central place in a model for waves on shallow water and it is an example of the propagation of weakly dispersive and weakly nonlinear waves. Its history spans a period of about sixty years, starting with experiments of Scott Russell in 1834, followed by theoretical investigations of, among others, Lord Rayleigh and Boussinesq in 1871 and, finally, Korteweg and De Vries in 1895. In this essay we compare the work of Boussinesq and Korteweg-de Vries, stressing essential differences and some interesting connections. Although there exist a number of articles, reviewing the origin and birth of the Korteweg-de Vries equations, connections and differences, not generally known, are reported.