Analytic study of a coupled Kerr-SBS system

In order to describe the coupling between the Kerr nonlinearity and the stimulated Brillouin scattering, Mauger et al. 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 single-valued 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.