On the asymptotic linearization of acoustic waves

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(e 2 ) in certain norms. The essential use is made of the fact that this equation is asymptotically linearizable to O(e 2 ), i.e., the equations can be mapped to an equation which differs from a linearizable equation only in terms which are of O(e 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.