THE COLLABORATION BETWEEN KORTEWEG AND DE VRIES — AN ENQUIRY INTO PERSONALITIES

arXiv:0710.5227v1 [physics.hist-ph] 27 Oct 2007

BASTIAAN WILLINK

Abstract. In the course of the years the names of Korteweg and de Vries have come to be closely associated. The equation which is named after them plays a fundamental role in the theory of nonlinear partial differential equations. What are the origins of the doctoral dissertation of De Vries and of the Korteweg-de Vries paper? Bastiaan Willink, a distant relative of both of these mathematicians, has sought to answer these questions. This article is based on a lecture delivered by the author at the symposium dedicated to Korteweg and de Vries at University of Amsterdam in September 2003.

Since its rediscovery by Zabusky and Kruskal in 1965, an extensive literature has come to exist on the Korteweg-de Vries equation (KdV equation) which describes the behavior of long-wavelength waves in shallow water. It is not the aim of this paper to add to the discussions concerning the contents of this equation or regarding the genesis of the theory of non-linear partial differential equations. Hereto Eduard de Jager has recently added two papers [1] Earlier Robert Pego and others questioned the originality of the work by De Vries and Korteweg, especially in relation to the work by Boussinesq [2]. De Jager has however made it plausible that although the KdV equation can be deduced from an equation of Boussinesq [Joseph Valentin Boussinesq (1842-1929)] by means of a relatively simple substitution, nonetheless Korteweg and De Vries arrived at new and important results through treading a different path than Boussinesq. In addition to the mathematical and hydrodynamical aspects of the discussion regarding the priority and originality, there are, however, other historical aspects to be considered. Anne Kox has earlier described Korteweg as the nexus between the physics and mathematics departments of University of Amsterdam and Ad