By Michiel Hazewinkel, Hans W. Capel, Eduard M. de Jager
Precisely 100 years in the past, in 1895, G. de Vries, lower than the supervision of D. J. Korteweg, defended his thesis on what's now referred to as the Korteweg--de Vries Equation. They released a joint paper in 1895 within the Philosophical journal, entitled `On the swap of type of lengthy waves advancing in an oblong canal, and on a brand new kind of lengthy desk bound wave', and, for the following 60 years or so, no different suitable paintings appeared to were performed. within the Nineteen Sixties, although, examine in this and comparable equations exploded. There are now a few 3100 papers in arithmetic and physics that comprise a point out of the word `Korteweg--de Vries equation' of their identify or summary, and there are hundreds of thousands extra in different components, akin to biology, chemistry, electronics, geology, oceanology, meteorology, and so on. And, after all, the KdV equation is just one of what are actually referred to as (Liouville) thoroughly integrable structures. The KdV and its kin regularly take place in occasions whilst one needs to comprise nonlinear and dispersive results into wave-type phenomena. This centenary offers a distinct party to survey as many alternative points of the KdV and comparable equations. The KdV equation has intensity, subtlety, and a breadth of functions that make it a rarity deserving detailed awareness and exposition.