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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
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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.
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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.
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