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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the asymptotic linearization of acoustic waves


Authors: Athanassios S. Fokas and Laihan Luo
Journal: Trans. Amer. Math. Soc. 360 (2008), 6403-6445
MSC (2000): Primary 35B40, 35C20, 35G25, 35Q53; Secondary 76B03, 76B15, 76M99
Published electronically: July 24, 2008
MathSciNet review: 2434293
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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 $ O(\epsilon^2)$ in certain norms. The essential use is made of the fact that this equation is asymptotically linearizable to $ O(\epsilon^2),$ i.e., the equations can be mapped to an equation which differs from a linearizable equation only in terms which are of $ O(\epsilon^2).$ 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: http://dx.doi.org/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
Published electronically: July 24, 2008
Additional Notes: This work was partially supported by the EPSRC, GR/J71885.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.