## On the asymptotic linearization of acoustic waves

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- by Athanassios S. Fokas and Laihan Luo PDF
- Trans. Amer. Math. Soc.
**360**(2008), 6403-6445 Request permission

## 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.## References

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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
- Received by editor(s): November 14, 2006
- Published electronically: July 24, 2008
- Additional Notes: This work was partially supported by the EPSRC, GR/J71885.
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**360**(2008), 6403-6445 - MSC (2000): Primary 35B40, 35C20, 35G25, 35Q53; Secondary 76B03, 76B15, 76M99
- DOI: https://doi.org/10.1090/S0002-9947-08-04531-5
- MathSciNet review: 2434293