One class of nonscattering acoustic shells for a model of anisotropic acoustics

We consider a model of linear acoustics describing diffraction of an acoustic wave on a local anisotropic inhomogeneity. Under study is the existence of inhomogeneities which do not scatter the incident acoustic fields that are generated by any exterior compactly supported sources. We prove the existence of the above-mentioned inhomogeneities. Some constructive way is given of constructing a class of anisotropic media depending on an arbitrary function of one variable. We obtain some explicit formulas that define the main parameters of the shell.