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Non-linear mechanisms in their gaseous or stellar component should govern the long-term behaviour of spiral galaxies. We derive the non-linear coupling of spiral or bar modes of different patterns speeds in an inhomogeneous stellar disc. Using classical WKBJ and epicyclic approximations for density waves, the non-linear perturbed densities and the corresponding, non-linearly modified, growth rate are computed. The presence of resonances in the region where modes overlap enhances this coupling, making it quite efficient at reasonably low amplitudes. Furthermore this mechanism provides a new way of closing the SWING or WASER amplification cycles for the coupled modes. This explains the results of recently published numerical simulations. Suggestions are then given for possible comparisons with certain observed barred spiral galaxies.
Sygnet et al. (Wed,) studied this question.