The propagation of polarization for systems of transversal type
The author considers systems of classical pseudodifferential operators of so-called transversal type. This means that microlocally the characteristic set is the union of two non-radial hypersurfaces, which have transversal involutive intersection at the double characteristics and, moreover, the principal symbol is of first-order on the two-dimensional kernel at the intersection. For this type of systems, the author investigates the propagation and distribution of polarization sets of solutions. The polarization set is a generalization of the wave front set and describes the components of the solution which are not smooth. The real polarizations at the double characteristic set, which by definition are limits of polarizations from outside this set, turn out to be foliated by limits of Hamiltonian orbits. The propagation of polarization is studied in this limit orbit case when the trace of the orbits satisfies a transport equation, moreover, when the polarization is transversal to the limit orbits and in the non-limit orbit case. Finally, the distributions of the polarizations in the different situations are considered.
scientific article; zbMATH DE number 894901