Normal forms of real symmetric systems with multiplicity. (English) Zbl 0802.35176

Braam, P. J.; Duistermaat, J. J.

Indag. Math., New Ser. 4, No. 4, 407-421 (1993).

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 \(D_ j = - i \partial/ \partial x_ j\).

Reviewer: B.Helffer (Paris)

MSC:

35S30	Fourier integral operators applied to PDEs
35A27	Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs

Keywords:

normal form; real symmetric systems of linear partial differential operators

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