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Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

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Book Information

Author(s): M. J. Ablowitz, B. Prinari and A. D. Trubatch
Title: Discrete and continuous nonlinear Schrödinger systems
Additional book information: Cambridge Univ. Press, Cambridge, 2004, ix+257, £38.00, 0-521-53437-2


References:

1.
M.J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM (Philadelphia, 1981). M.J. Ablowitz and P.A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press (Cambridge, 1991). MR 0642018 (84a:35251), MR 1149378 (93g:35108)

2.
M.J. Ablowitz, B. Prinari and A.D. Trubatch, Discrete and Continuous Nonlinear Schrödinger Systems, Cambridge University Press (Cambridge, 2004). MR 2040621 (2005c:37117)

3.
C. Sulem and P.L. Sulem,
The Nonlinear Schrödinger Equation, Springer-Verlag (New York, 1999). MR 1696311 (2000f:35139)

4.
A. Hasegawa, Solitons in Optical Communications, Clarendon Press (Oxford, NY, 1995).

5.
B.A. Malomed, Variational methods in nonlinear fiber optics and related fields, Progress in Optics 43 (2002) 69-191.

6.
V.E. Zakharov, Collapse and Self-focusing of Langmuir Waves,
Handbook of Plasma Physics, (M.N. Rosenbluth and R.Z. Sagdeev, eds.), vol. 2 (A.A. Galeev and R.N. Sudan, eds.) 81-121, Elsevier (1984).

7.
V.E. Zakharov, Collapse of Langmuir waves, Sov. Phys. JETP 35 (1972) 908-914.

8.
T.B. Benjamin and J.E. Feir, The disintegration of wavetrains in deep water, Part 1, J. Fluid Mech. 27 (1967) 417-430.

9.
M. Onorato, A.R. Osborne, M. Serio, and S. Bertone, Freak waves in random oceanic sea states, Phys. Rev. Lett. 86 (2001) 5831-5834.

10.
H. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd and J.S. Aitchinson, Discrete Spatial Optical Solitons in Waveguide Arrays, Phys. Rev. Lett. 81 (1998) 3383-3386; H. Eisenberg, Y. Silberberg, R. Morandotti and J.S. Aitchinson, Diffraction Management 85 (2000) 1863-1866.

11.
J. Meier, G.I. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Nonlinear Optical Beam Interactions in Waveguide Arrays, Phys. Rev. Lett. 93 (2004) 093903.

12.
F. Dalfovo, S. Giorgini, L.P. Pitaveskii and S. Stringari, Rev. Mod. Phys. 71 (1999) 463-512.

13.
P.G. Kevrekidis and D.J. Frantzeskakis, Pattern forming dynamical instabilities of Bose-Einstein condensates, Mod. Phys. Lett. B 18 (2004) 173-202; P.G. Kevrekidis, R. Carretero-González, D.J. Frantzeskakis, I.G. Kevrekidis, Vortices in Bose-Einstein condensates: some recent developments, Mod. Phys. Lett. B 18 (2004) 1481-1505.

14.
V.A. Brazhnyi and V.V. Konotop, Theory of nonlinear matter waves in optical lattices, Mod. Phys. Lett. B 18 (2004) 627-651.

15.
G. L. Alfimov, P. G. Kevrekidis, V. V. Konotop, and M. Salerno, Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential, Phys. Rev. E 66 (2002) 046608. MR 1935204 (2003j:81003)

16.
M.J. Ablowitz and Z.H. Musslimani, Discrete spatial solitons in a diffraction-managed nonlinear waveguide array: a unified approach, Physica D 184 (2003) 276-303. MR 2030690 (2004k:78020)

17.
B.P. Anderson and M.A. Kasevich, Macroscopic quantum interference from atomic tunnel arrays, Science 282 (1998) 1686-1689.

18.
K.S. Strecker, G.B. Partridge, A.G. Truscott, and R.G Hulet, Formation and propagation of matter wave soliton trains, Nature 417 (2002) 150-153.

19.
H. Ott, J. Fortágh, S. Kraft, A. Günther, D. Komma, and C. Zimmermann, Nonlinear dynamics of a Bose-Einstein condensate in a magnetic waveguide, Phys. Rev. Lett. 91 (2003) 040402.

20.
A.S. Desyatnikov, L. Torner and Yu.S. Kivshar, Optical vortices and vortex solitons, nlin.PS/0501026.

21.
R.S. MacKay and S. Aubry, Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators,
Nonlinearity 7 (1994) 1623-1643. MR 1304442 (96a:34085)

22.
M.J. Ablowitz and J.F. Ladik, Nonlinear differential-difference equations, J. Math. Phys. 16 (1975) 598-603; M.J. Ablowitz and J.F. Ladik, Nonlinear differential-difference equations and Fourier analysis, J. Math. Phys. 17 (1976) 1011-1018. MR 0377223 (51:13396), MR 0427867 (55:897)

23.
T. Kapitula and P. Kevrekidis, Stability of waves in discrete systems, Nonlinearity 14 (2001) 533-566. MR 1830906 (2002f:37116)

24.
S.V. Manakov, On the theory of two-dimensional stationary self-focusing of electromagnetic waves, Sov. Phys. JETP 38 (1974) 248-253.

25.
M.J. Ablowitz, Y. Ohta and A.D. Trubatch, Phys. Lett. A 253 (1999) 287-304. MR 1681692 (99m:35215)

26.
Yu.S. Kivshar and G.P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals, Academic Press (San Diego, 2003).

27.
L.P. Pitaevskii and S. Stringari, Bose-Einstein Condensation, Oxford University Press (Oxford, 2003). MR 2012737 (2004i:82038)

28.
C.J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases, Cambridge University Press (Cambridge, 2002).


Additional Information:

Reviewer(s):
P. G. Kevrekidis
Affiliation: University of Massachusetts
Email: kevrekid@math.umass.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 43 (2006), 127-132.

MSC (2000): Primary 35Q55
DOI: 10.1090/S0273-0979-05-01074-8
PII: S 0273-0979(05)01074-8
Posted: July 8, 2005
Dedicated: The author was supported in part by NSF-DMS-0204585 and NSF-CAREER.
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


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