The theory of soliton equations and integrable systems has
developed rapidly during the last 20 years with numerous
applications in mechanics and physics. For a long time books in
this field have not been written but the flood of papers was
overwhelming: many hundreds, maybe thousands of them. All this
followed one single work by Gardner, Greene, Kruskal, and Miura
about the Korteweg-de Vries equation (KdV) which, had seemed to be
merely an unassuming equation of mathematical physics describing
waves in shallow water.
This branch of science is attractive because it is one of those
which revives the interest in the basic principles of mathematics,
a beautiful formula.
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