On the asymptotic linearization of acoustic waves

Fokas, Athanassios; Luo, Laihan

doi:10.1090/S0002-9947-08-04531-5

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.

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