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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

MathSciNet review: 3497800
Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: B. Grébert and T. Kappeler
Title: The defocusing NLS equation and its normal form
Additional book information: EMS Series of Lectures in Mathematics, European Mathematical Society (EMS), Z\"urich, 2014, x+166 pp., ISBN 978-3-03719-131-6, US$38.00

References [Enhancements On Off] (What's this?)

  • D. Bättig, A. M. Bloch, J.-C. Guillot, and T. Kappeler, On the symplectic structure of the phase space for periodic KdV, Toda, and defocusing NLS, Duke Math. J. 79 (1995), no. 3, 549–604. MR 1355177, DOI 10.1215/S0012-7094-95-07914-9
  • B. A. Dubrovin, V. B. Matveev, and S. P. Novikov, Nonlinear equations of Korteweg-de Vries type, finite-band linear operators and Abelian varieties, Uspehi Mat. Nauk 31 (1976), no. 1(187), 55–136 (Russian). MR 0427869
  • B. A. Dubrovin and S. P. Novikov, Periodic and conditionally periodic analogs of the many-soliton solutions of the Korteweg-de Vries equation, Ž. Èksper. Teoret. Fiz. 67 (1974), no. 6, 2131–2144 (Russian, with English summary); English transl., Soviet Physics JETP 40 (1974), no. 6, 1058–1063. MR 0382877
  • B. A. Dubrovin, A periodic problem for the Korteweg-de Vries equation in a class of short-range potentials, Funkcional. Anal. i Priložen. 9 (1975), no. 3, 41–51 (Russian). MR 0486780
  • H. Flaschka and D. W. McLaughlin, Canonically conjugate variables for the Korteweg-de Vries equation and the Toda lattice with periodic boundary conditions, Progr. Theoret. Phys. 55 (1976), no. 2, 438–456. MR 403368, DOI 10.1143/PTP.55.438
  • Thomas Kappeler, Fibration of the phase space for the Korteweg-de Vries equation, Ann. Inst. Fourier (Grenoble) 41 (1991), no. 3, 539–575 (English, with French summary). MR 1136595
  • Thomas Kappeler and Jürgen Pöschel, KdV & KAM, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 45, Springer-Verlag, Berlin, 2003. MR 1997070, DOI 10.1007/978-3-662-08054-2
  • H. P. McKean and K. L. Vaninsky, Action-angle variables for the cubic Schrödinger equation, Comm. Pure Appl. Math. 50 (1997), no. 6, 489–562. MR 1441912, DOI 10.1002/(SICI)1097-0312(199706)50:6<489::AID-CPA1>3.0.CO;2-4
  • N. J. Zabusky and M. D. Kruskal, Interaction of solitons in a collisionless plasma and the recurrence of initial states, Phys. Rev. Lett. 15 (1965), 240–243.

  • Review Information:

    Reviewer: Dario Bambusi
    Affiliation: Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy
    Email: dario.bambusi\
    Journal: Bull. Amer. Math. Soc. 53 (2016), 337-342
    Published electronically: October 8, 2015
    Review copyright: © Copyright 2015 American Mathematical Society