Abstract
We study several methods of describing ‘explicit’ solutions to equations of Korteweg-de Vries type: (i) the method of algebraic geometry (Krichever, I.M.
Usp. mat. Nauk
32, 183-208 (1977)); (ii) the Grassmannian formalism of the Kyoto school (iii) acting on the trivial solution by the ‘group of dressing transformations’ (Zakharov, V. E. & Shabat, A. B.
Funct. Anal. Appl.
13 (3), 13-22 (1979)). I show that the three methods are more or less equivalent, and in particular that the ‘
r
-functions’ of method (ii) arise very naturally in the context of method (iii).
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