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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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


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:
  • Laihan Luo
  • Affiliation: Department of Mathematics, New York Institute of Technology, 1855 Broadway, New York, New York 10023
  • Email:
  • 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:
  • MathSciNet review: 2434293