Scattering problems for differential operators with perturbation of the space

For differential operators with constant coefficients in $R^m$ we study the existence and completeness of wave operators corresponding to perturbation of the metric of the original Hilbert space. The results are applied, in particular, to scattering problems of Maxwell's system in an anisotropic medium and for the wave equation. The study is based on abstract criteria (of “nuclear type”) of existence of complete wave operators.