Lax equation representation of certain completely integrable systems

Leon D. Fairbanks

Compositio Mathematica (1988)

  • Volume: 68, Issue: 1, page 31-40
  • ISSN: 0010-437X

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Fairbanks, Leon D.. "Lax equation representation of certain completely integrable systems." Compositio Mathematica 68.1 (1988): 31-40. <http://eudml.org/doc/89928>.

@article{Fairbanks1988,
author = {Fairbanks, Leon D.},
journal = {Compositio Mathematica},
keywords = {Lax representations; completely integrable system; Kovalevskaya top},
language = {eng},
number = {1},
pages = {31-40},
publisher = {Kluwer Academic Publishers},
title = {Lax equation representation of certain completely integrable systems},
url = {http://eudml.org/doc/89928},
volume = {68},
year = {1988},
}

TY - JOUR
AU - Fairbanks, Leon D.
TI - Lax equation representation of certain completely integrable systems
JO - Compositio Mathematica
PY - 1988
PB - Kluwer Academic Publishers
VL - 68
IS - 1
SP - 31
EP - 40
LA - eng
KW - Lax representations; completely integrable system; Kovalevskaya top
UR - http://eudml.org/doc/89928
ER -

References

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  1. 1 M. Adler and P. van Moerbeke: Completely integrable systems, Euclidean lie algebras, and curves, Advances in Math.38 (1980) 267-317. Zbl0455.58017MR597729
  2. 2 M. Alder and P. van Moerbeke: The identification of the Kowaleski top and the Manchow flow of SO(4) and a family of Kac-Moody Lax Pairs for the Kowalewski top, Preprint (1987). 
  3. 3 M. Buys: The Kovalevskaya top, Thesis, NYU (1982). 
  4. 4 B.A. Dubrovin: Theta functions and non-linear equations, Russian Math. Surveys36:2 (1980) 11-92. Zbl0549.58038MR616797
  5. 5 B.A. Dubrovin, A.T. Fomenko and S.P. Novikov: Modern Geometry - Methods and Applications, Part II, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo (1984) 337-344. Zbl0529.53002MR736837
  6. 6 P.A. Griffiths: Linearizing flows and a cohomological interpretation of Lax equations, Amer. J. of Math.107 (1985) 1445-1483. Zbl0585.58028MR815768
  7. 7 P.A. Griffiths and J. Harris: Principles of Algebraic Geometry, John Wiley and Sons, New York, Chichester, Brisbane, Toronto (1978). Zbl0408.14001MR507725
  8. 8 L. Haine and E. Horozov: A Lax Pair for Kowalewski's top, Preprint (1987). Zbl0627.58026MR923889
  9. 9 S. Kovalevskaya, Sur le probleme de la rotation d'un corps solide autour d'un point fixe, Acta Math.12 (1889) 127-232. JFM21.0935.01
  10. 10 D. Mumford: Tata Lectures on Theta, Volume II, Birkäuser, Boston, Basel, Stuttgart (1984). Zbl0549.14014MR742776
  11. 11 E. Previato: Generalized Weierstrass p-functions and KP flows in affine space, Comm. Math. Helvetici62 (1987) 292-310. Zbl0638.14024MR896099
  12. 12 A. Reyman and M. Semonov-Tianshansky: Lax representations with a spectral parameter for the Kovalevskaya top and its generalizations, Preprint (1987). 
  13. 13 G. Segal and G. Wilson: Loop groups and equations of KdV type, Publications Mathématiques de l'Institute des Hautes Études61 (1985). Zbl0592.35112MR783348
  14. 14 J.L. Verdier: Algebres de Lie, Systems Hamiltoniens, courbes algebriques, Seminaire Bourbaki566 (1980/81). Zbl0492.58014

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