|
On the asymptotic linearization of acoustic waves
Author(s):
Athanassios
S.
Fokas;
Laihan
Luo
Journal:
Trans. Amer. Math. Soc.
360
(2008),
6403-6445.
MSC (2000):
Primary 35B40, 35C20, 35G25, 35Q53;
Secondary 76B03, 76B15, 76M99
Posted:
July 24, 2008
MathSciNet review:
2434293
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
The initial value problem of a certain generalization of the nonlinear, dispersive wave equations with dissipation is rigorously studied. The solutions of the equations can be found exactly up to  in certain norms. The essential use is made of the fact that this equation is asymptotically linearizable to  i.e., the equations can be mapped to an equation which differs from a linearizable equation only in terms which are of  An application of the equations to unidirectional small amplitude acoustic waves is discussed. The general methodology used here can also be applied to other asymptotically linearizable equations.
References:
-
- 1.
- C.J. Amick, J.L. Bona and M.E. Schonbek, Decay of solutions of some nonlinear wave equations, J. Differential Equations 81 (1989), pp. 1-49. MR 1012198 (90k:35210)
- 2.
- J.L. Bona and L. Luo, More Results on the Decay of Solutions to Nonlinear, Dispersive Wave Equations, Discrete and Continuous Dynamical Systems 1 (1995), pp. 151-193. MR 1355869 (96h:35177)
- 3.
- P. Deift, A.R. Its and X. Zhou, in Important Developments in Soliton Theory, A.S. Fokas and V.E. Zakharov (eds.), Springer-Verlag, 1993. MR 1280466 (95a:58002)
- 4.
- R.K. Dodd, J.C. Eilbeck, J.D. Gibbon and H.C. Morris, Solutions and Nonlinear Wave Equations, Academic Press, London, 1982. MR 696935 (84j:35142)
- 5.
- A.S. Fokas and B. Fuchssteiner, The Hierarchy of the Benjamin-Ono Equation, Phys. Lett. A 86 (1981), pp. 341-345. MR 637024 (83f:58039)
- 6.
- A.S. Fokas and Q.M. Liu, Asymptotic Integrability of Water Waves, Phys. Rev. Lett. 77 (1996), pp. 2347-2351. MR 1406987 (97f:76009)
- 7.
- A.S. Fokas and L. Luo, On the Asymptotic Integrability of a Generalized Burgers Equation, in Hydrodynamic Waves, Contemporary Mathematics, Vol. 200 (Dias, Ghidaglia and Saut, eds.), American Mathematical Society, Providence, RI (1996), pp. 85-98. MR 1410502 (98b:35156)
- 8.
- Y. Kodama, On Integrable Systems with Higher Order Corrections, Phys. Lett. A 107 (1985), pp. 245-249; and Nearly Integrable Systems, Physica D 16 (1985), pp. 14-26. MR 778808 (86i:58065)
- 9.
- Q.M. Liu, Ph.D. Dissertation, Clarkson University, 1995.
- 10.
- G.B. Whitham, Linear and Nonlinear Waves, Wiley, New York, 1974. MR 0483954 (58:3905)
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (2000):
35B40, 35C20, 35G25, 35Q53,
76B03, 76B15, 76M99
Retrieve articles in all Journals with
MSC (2000):
35B40, 35C20, 35G25, 35Q53,
76B03, 76B15, 76M99
Additional Information:
Athanassios
S.
Fokas
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, United Kingdom
Email:
T.Fokas@damtp.cam.ac.uk
Laihan
Luo
Affiliation:
Department of Mathematics, New York Institute of Technology, 1855 Broadway, New York, New York 10023
Email:
lluo@nyit.edu
DOI:
10.1090/S0002-9947-08-04531-5
PII:
S 0002-9947(08)04531-5
Keywords:
Nonlinear,
dissipation,
dispersive,
wave,
asymptotic linearization
Received by editor(s):
November 14, 2006
Posted:
July 24, 2008
Additional Notes:
This work was partially supported by the EPSRC, GR/J71885.
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
