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Infinite-Dimensional Lie Groups and Algebraic Geometry in Soliton Theory
Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 315, No. 1533, New Developments in the Theory and Application of Solitons (Aug. 13, 1985), pp. 393-404
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/37541
Page Count: 12
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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 `τ -functions' of method (ii) arise very naturally in the context of method (iii).
Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences © 1985 Royal Society