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Book Review
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Book Information
Author(s):
Fritz Gesztesy and Helge Holden
Title:
Soliton equations and their algebro-geometric solutions. Vol. I.  -dimensional continuous models
Additional book information:
Cambridge Studies in Advanced Mathematics, 79, Cambridge University Press,
Cambridge,
2003,
xii+505 pp.,
US$117.00,
ISBN 0-521-75307-4
References:
-
- [B]
- J. Boussinesq, Théorie générale des mouvements qui sont propagés dans un canal rectangulaire horizontal, C. R. Acad. Sci. Paris Sér. I Math. 73 (1871), 256-260 (JFM 03.0486.02).
- [DKN]
- B.A. Dubrovin, I.M. Krichever and S.P. Novikov, Integrable systems. I. Current problems in mathematics. Fundamental directions, Vol. 4, 179-284, 291, Akad. Nauk SSSR, Moscow, 1985. MR 842910 (87k:58112)
- [FT]
- L.D. Faddeev and L.A. Takhtajan, Hamiltonian methods in the theory of solitons, Springer, Berlin, 1987. MR 905674 (89m:58103)
- [GGKM]
- C.S. Gardner, J.M. Greene, M.D. Kruskal and R. M. Miura, Korteweg-deVries equation and generalizations. VI. Methods for exact solution, Comm. Pure Appl. Math. 27 (1974), 97-133. MR 0336122 (49:898)
- [GD]
- I.M. Gel'fand and L.A. Dikiı, Asymptotic properties of the resolvent of Sturm-Liouville equations, and the algebra of Korteweg-de Vries equations, Uspehi Mat. Nauk 30 (1975), 67-100. MR 0508337 (58:22746)
- [H]
- R.W. Hamming, The unreasonable effectiveness of mathematics, Amer. Math. Monthly 87 (1980), 81-90. MR 559142 (81e:00015)
- [KDV]
- D.J. Korteweg and G. De Vries, On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Phil. Mag. (5) XXXIX (1895), 422-443. JFM 26.0881.02
- [P]
- R.S. Palais, The symmetries of solitons, Bull. Amer. Math. Soc. (N.S.) 34 (1997), 339-403. MR 1462745 (98f:58111)
- [S]
- M. Sato, The KP hierarchy and infinite-dimensional Grassmann manifolds, Proc. Sympos. Pure Math. 49, pp. 51-66, Amer. Math. Soc., Providence, RI, 1989. MR 1013125 (91d:58107)
Additional Information:
Reviewer(s):
Emma
Previato
Affiliation:
Boston University
Email:
ep@bu.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
45
(2008),
459-467.
MSC
(2000):
Primary 37K40;
Secondary 14H70, 34L05, 35Q53
DOI:
10.1090/S0273-0979-08-01179-8
PII:
S 0273-0979(08)01179-8
Posted:
January 7, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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