  We present a general formalism which allows us to derive the evolution
equations describing one-dimensional (1D) and isotropic 2D interfacelike
systems, that is based on symmetries, conservation laws, multiple scale
arguments, and exploits the relevance of coarsening dynamics. Our approach
becomes especially significant in the presence of surface morphological
instabilities and allows us to classify the most relevant nonlinear terms in
the continuum description of these systems. The formalism applies to systems
ranging from eroded nanostructures to macroscopic pattern formation. In
particular, we show the validity of the theory for novel experiments on ion
plasma erosion.
