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A novel local evolution equation for one-dimensional interfaces is derived inthe context of erosion by ion beam sputtering. We present numerical simulationsof this equation which show interrupted coarsening in which an ordered cellpattern develops with constant wavelength and amplitude at intermediatedistances, while the profile is disordered and rough at larger distances.Moreover, for a wide range of parameters the lateral extent of ordered domainsranges up to tens of cells. This behavior is new in the context of dynamics ofsurfaces or interfaces with morphological instabilities. We also provideanalytical estimates for the stationary pattern wavelength and mean growthvelocity

Short-range stationary patterns and long-range disorder in an evolution equation for one-dimensional interfaces