Asymptotic step profiles from a nonlinear growth equation for vicinal surfaces

We study a recently proposed nonlinear evolution equation describing the co llective step meander on a vicinal surface subject to the Bales-Zangwill gr owth instability [O. Pierre-Louis et al., Phys. Rev. Lett. 80, 4221 (1998)] . A careful numerical analysis shows that the dynamically selected step pro file consists of sloped segments, given by an inverse error function and st eepening as roott, which are matched to pieces of a stationary (time-indepe ndent) solution describing the maxima and minima. The effect of smoothening by step-edge diffusion is included heuristically, and a one-parameter fami ly of evolution equations is introduced that contains relaxation by step-ed ge diffusion and by attachment-detachment as special cases. The question of the persistence of an initially imposed meander wavelength is investigated in relation to recent experiments.