Normal forms of real symmetric systems with multiplicity (Q1319090)

A normal form is given for real symmetric systems of linear partial differential operators where the principal symbol has a two-dimensional kernel under assumptions which apply to the generic case. The model is microlocally the following \(2\times 2\) system: \[ \left( \begin{matrix} D_ 1 + D_ 2 & x_ 2D_ 3\\ x_ 2D_ 3 & \pm(D_ 1 - D_ 2) \end{matrix} \right) \] with \(D_ j = - i \partial/ \partial x_ j\).