  In order to describe the coupling between the Kerr nonlinearity and the
stimulated Brillouin scattering, Mauger et alii recently proposed a system of
partial differential equations in three complex amplitudes. We perform here its
analytic study by two methods. The first method is to investigate the structure
of singularities, in order to possibly find closed form singlevalued solutions
obeying this structure. The second method is to look at the infinitesimal
symmetries of the system in order to build reductions to a lesser number of
independent variables. Our overall conclusion is that the structure of
singularities is too intricate to obtain closed form solutions by the usual
methods. One of our results is the proof of the nonexistence of traveling
waves.
