  Motivated by the increasing interest in the properties of multimode
optomechanical devices, here we study a system in which a driven mode of a
large-area optical cavity is despersively coupled to a deformable mechanical
element. Two different models naturally appear in such scenario, for which we
predict the formation of periodic patterns, localized structures (cavity
solitons), and domain walls, among other complex nonlinear phenomena. Further,
we propose a realistic design based on intracavity membranes where our models
can be studied experimentally. Apart from its relevance to the field of
nonlinear optics, the results put forward here are a necessary step towards
understanding the quantum properties of optomechanical systems in the multimode
regime of both the optical and mechanical degrees of freedom.
