Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Infinite-Dimensional Lie Groups and Algebraic Geometry in Soliton Theory

G. Wilson
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
  • Read Online (Free)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Infinite-Dimensional Lie Groups and Algebraic Geometry in Soliton Theory
Preview not available

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 `τ -functions' of method (ii) arise very naturally in the context of method (iii).

Page Thumbnails

  • Thumbnail: Page 
393
    393
  • Thumbnail: Page 
394
    394
  • Thumbnail: Page 
395
    395
  • Thumbnail: Page 
396
    396
  • Thumbnail: Page 
397
    397
  • Thumbnail: Page 
398
    398
  • Thumbnail: Page 
399
    399
  • Thumbnail: Page 
400
    400
  • Thumbnail: Page 
401
    401
  • Thumbnail: Page 
402
    402
  • Thumbnail: Page 
403
    403
  • Thumbnail: Page 
404
    404