Enhancement of a general solution to Lighthill-Westervelt nonlinear acoustic equation to the cases of inhomogeneous and random media

Abstract

A general solution to the Lighthill-Westervelt equation of nonlinear acoustics, previously developed and successfully applied to model the scattering of sound by sound and to the parametric array, has been generalized further for use in the cases of inhomogeneous and random media. The form of the solution makes use of an exact inverse differential operator in combination with a sequence of perturbation terms that comprise the multiple orders of nonlinear acoustic scattering to arbitrary order. Integration techniques have been developed which allow accurate, approximate, analytical solutions under particular circumstances. These solutions are shown to reduce to other previously known solutions in the appropriate limits.