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Book Review

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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), Zürich, 2014, x+166 pp., ISBN 978-3-03719-131-6, US$38.00

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

  • [BBGK95] 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 (96i:58065), https://doi.org/10.1215/S0012-7094-95-07914-9
  • [DMN76] 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 (55 #899)
  • [DN74] 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 (52 #3759)
  • [Dub75] 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 (58 #6480)
  • [FM76] 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 0403368 (53 #7179)
  • [Kap91] 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 (92k:58212)
  • [KP03] 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 (2004g:37099)
  • [MV97] 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 (98b:35183), https://doi.org/10.1002/(SICI)1097-0312(199706)50:6$ \langle $489::AID-CPA1$ \rangle $3.0.CO;2-4
  • [ZK65] 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\string @unimi.it
Journal: Bull. Amer. Math. Soc. 53 (2016), 337-342
MSC (2010): Primary 35Q55, 37K10, 37K55
DOI: https://doi.org/10.1090/bull/1522
Published electronically: October 8, 2015
Review copyright: © Copyright 2015 American Mathematical Society
American Mathematical Society