Scattering of acoustic waves by a coated pressure-release ellipsoid

We consider low-frequency scattering by a penetrable ellipsoid with a soft confocal ellipsoidal core. The second-order terms for the field and the fourth-order terms for the scattering amplitude are obtained. Physically degenerate forms, such as the penetrable, the rigid, and the soft ellipsoid as well as special geometrical cases, such as spheroids, sphere, needle, and disk, are obtained by assigning appropriate values to the physical and geometrical parameters of the problem.