Asymptotic step profiles from a nonlinear growth equation for vicinal surfaces

We study a recently proposed nonlinear evolution equation describing the collective step meander on a vicinal surface subject to the Bales-Zangwill growth instability [O. Pierre-Louis et al., Phys. Rev. Lett. 80, 4221 (1998)]. A careful numerical analysis shows that the dynamically selected step profile consists of sloped segments, given by an inverse error function and steepening as roott, which are matched to pieces of a stationary (time-independent) solution describing the maxima and minima. The effect of smoothening by step-edge diffusion is included heuristically, and a one-parameter family of evolution equations is introduced that contains relaxation by step-edge 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.