Book Review
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Book Information:
Authors:
P. I. Naumkin and
I. A. Shishmarev
Title:
Nonlinear nonlocal equations in the theory of waves
Additional book information:
Transl. Math. Monographs, vol. 133, Amer. Math. Soc.,
Providence, RI,
1994,
x+289 pp.,
ISBN 0-8218-4753-X,
$149.00$
Mark J. Ablowitz and Harvey Segur, Solitons and the inverse scattering transform, SIAM Studies in Applied Mathematics, vol. 4, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa., 1981. MR 642018
C. J. Amick, J. L. Bona, and M. E. Schonbek, Decay of solutions of some nonlinear wave equations, J. Differential Equations 81 (1989), no. 1, 1–49. MR 1012198, DOI 10.1016/0022-0396(89)90176-9
P. Deift, S. Venakides, and X. Zhou, The collisionless shock region for the long-time behavior of solutions of the KdV equation, Comm. Pure Appl. Math. 47 (1994), no. 2, 199–206. MR 1263128, DOI 10.1002/cpa.3160470204
Daniel B. Dix, Temporal asymptotic behavior of solutions of the Benjamin-Ono-Burgers equation, J. Differential Equations 90 (1991), no. 2, 238–287. MR 1101240, DOI 10.1016/0022-0396(91)90148-3
Daniel B. Dix, The dissipation of nonlinear dispersive waves: the case of asymptotically weak nonlinearity, Comm. Partial Differential Equations 17 (1992), no. 9-10, 1665–1693. MR 1187625, DOI 10.1080/03605309208820899
[D3] -, Large-time asymptotic behavior of solutions of linear dispersive equations, preprint.
T. Venkatarayudu, The $7$-$15$ problem, Proc. Indian Acad. Sci., Sect. A. 9 (1939), 531. MR 0000001, DOI 10.1090/gsm/058
Joel Smoller, Shock waves and reaction-diffusion equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 258, Springer-Verlag, New York-Berlin, 1983. MR 688146
G. B. Whitham, Linear and nonlinear waves, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. MR 0483954
- [AS]
- M. Ablowitz and H. Segur, Solitons and the inverse scattering transform, SIAM, Philadelphia, 1981. MR 0642018
- [ABS]
- C. Amick, J. Bona, and M. Schonbek, Decay of solutions of some nonlinear wave equations, J. Diff. Eq. 81 (1989), 1-49. MR 1012198
- [DVZ]
- P. Deift, S. Venakides, and X. Zhou, The collisionless shock region for the long-time behavior of solutions of the KdV equation, Comm. Pure Appl. Math. 47 (1994), 199-206. MR 1263128
- [D1]
- D. Dix, Temporal asymptotic behavior of solutions of the Benjamin-Ono-Burgers equation, J. Diff. Eq. 90 (1991), 238-287. MR 1101240
- [D2]
- -, The dissipation of nonlinear dispersive waves: the case of asymptotically weak nonlinearity, Comm. Part. Diff. Eqns. 17 (1992), 1665-1693. MR 1187625
- [D3]
- -, Large-time asymptotic behavior of solutions of linear dispersive equations, preprint.
- [K]
- S. Kichenassamy, Nonlinear wave equations, Marcel Dekker, New York, 1996.
MR 1:362 547
- [S]
- J. Smoller, Shock waves and reaction-diffusion equations, Springer-Verlag, New York, 1982. MR 0688146
- [W]
- G. Whitham, Linear and nonlinear waves, John Wiley and Sons, New York, 1974. MR 0483954
Review Information:
Reviewer:
John P. Albert
Affiliation:
University of Oklahoma
Email:
jalbert@uoknor.edu
Journal:
Bull. Amer. Math. Soc.
34 (1997), 95-100
DOI:
https://doi.org/10.1090/S0273-0979-97-00705-2
Review copyright:
© Copyright 1997
American Mathematical Society
