Titlebook: KdV ’95; Proceedings of the I Michiel Hazewinkel,Hans W. Capel,Eduard M. Jager Conference proceedings 1995 Springer Science+Business Media

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978-94-010-4011-2Springer Science+Business Media Dordrecht 1995

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An ODE to a PDE: Glories of the KdV Equation. An Appreciation of the Equation on Its 100th Birthday!Though you may not believe me, I am normally of a shy and retiring disposition, modest to a fault, even timid at times. Therefore it is difficult for me to bring myself to make the following bold claim, but I must do so in the interest of the Higher Truth.

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Instructive History of the Quantum Inverse Scattering Methodwas described in a short and famous research letter by Gardner, Green, Kruskal, and Miura (GGKM) [2] in 1967. Its quantum version, which is ten years younger, was devised mostly in Leningrad (now St. Petersburg). In what follows, I shall underline some highlights and lessons of this latter development.

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Korteweg, de Vries, and Dutch Science at the Turn of the Centuryes, which was defended on 1 December 1894 at the Amsterdam University [1]. That the centenary of the equation is nevertheless celebrated in 1995, instead of in 1994, has a good reason: the work of Korteweg and de Vries became internationally known through a joint paper they published in May 1895 [2].

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A KdV Equation in 2 + 1 Dimensions: Painlevé Analysis, Solutions and Similarity Reductionshe Darboux—Moutard—Matveev formalism arises in the context of this analysis. Some solutions and their interactions are also analyzed. The singular manifold equations are also used to determine symmetry reductions. This procedure can be related with the direct method of Clarkson and Kruskal.