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 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:
https://doi.org/10.1090/S0002-9947-08-04531-5

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.