American Mathematical Society

Book Review

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MathSciNet review: 3497800
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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), Z\"urich, 2014, x+166 pp., ISBN 978-3-03719-131-6, US$38.00

References

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 https://doi.org/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 https://doi.org/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
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 https://doi.org/10.1002/%28SICI%291097-0312%28199706%2950%3A6%3C489%3A%3AAID-CPA1%3E3.0.CO%3B2-4

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\string@unimi.it