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Intended to give a self-consistent outline of new analytical prospects that deal with the laser dynamics issue, from which results that go beyond the well-known linear stability analysis are extracted. The method of investigation is rooted in weak and strong- harmonic Fourier-expansions applied to the laser equations when these operate under unstable conditions. Both routines are shown to apply equally well to the simple Lorenz-Haken model as well as to the much complex integro-differential Maxwel-Bloch equations.
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