Korteweg and de vries

Pages: 32 (7764 mots) Publié le: 24 mars 2011

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


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 theorigins 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 in1965, 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 twopapers [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 Vriesarrived 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 AdMaas has considered him as a transitional figure in the mathematical and academic traditions [3]. In this paper I shall go into the personal backgrounds of both Korteweg and De Vries which will shed new light on the peculiar genesis of De Vries’ doctoral dissertation (proefschrift) and the KdV paper. Whereas Korteweg is known as a Dutch pioneer in the area of scientific bibliography, it appears,paradoxically, that some matters may have gone amiss with the digestion of the international literature by his doctoral student (promovendus) Gustav de Vries. It appears grotesque that while Korteweg, who has played an important role in the professionalization of the exact sciences in the Netherlands, would have somehow neglected appropriately to supervise one his doctoral students, one of the essentialparts of his responsibilities as a university professor. That Korteweg and De Vries were of flesh and blood will become apparent from their biographies to be presented below, which make
Received by the editors October 27, 2007.



the remarkable events surrounding De Vries’ doctoral research (promotie) more understandable. In a footnote in my book ‘De Tweede GoudenEeuw’ (The Second Golden Age) I published a letter from the supervisor [Korteweg] to the doctoral student [De Vries] which at the very least elicits astonishment [4]. The letter dates from October 1893, one year before the graduation (promotie) of De Vries on 1 December 1894. Because of its historical interest, I again cite it here: “Dear Sir, To my regret I am unable to accept your dissertation inits present form. It contains too much translated material, where you follow Rayleigh and McCowan to the letter. The remarks and clarifications that you introduce now and then, do not compensate for this shortcoming. The study of the literature concerning your subject-matter must serve solely as a means for arriving at a more independent treatment [‘whereby you’ is put in by mistake, B.W.],...
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