  Regular spatial structures emerge in a wide range of different dynamics
characterized by local and/or nonlocal coupling terms. In several research
fields this has spurred the study of many models, which can explain pattern
formation. The modulations of patterns, occurring on long spatial and temporal
scales, can not be captured by linear approximation analysis. Here, we show
that, starting from a general model with long range couplings displaying
patterns, the spatio-temporal evolution of large scale modulations at the onset
of instability is ruled by the well-known Ginzburg-Landau equation,
independently of the details of the dynamics. Hence, we demonstrate the
validity of such equation in the description of the behavior of a wide class of
systems. We introduce a novel mathematical framework that is also able to
retrieve the analytical expressions of the coefficients appearing in the
Ginzburg-Landau equation as functions of the model parameters. Such framework
can include higher order nonlocal interactions and has much larger
applicability than the model considered here, possibly including pattern
formation in models with very different physical features.
