Kink dynamics in a one-dimensional growing surface

A high-symmetry crystal surface may undergo a kinetic instability during the growth, such that its late stage evolution resembles a phase separation process. Th.is parallel is rigorous in one dimension, if the conserved surface current is derivable from a free energy. We study the problem in the presence of a physically relevant term breaking the up-down symmetry of the surface and that cannot be derived from a free energy: Following the treatment introduced by Kawasaki and Ohta [Physica A 116, 573 (1982)] for the symmetric case, we are able to translate the problem of the surface evolution into a problem of nonlinear dynamics of I;inks (domain walls). Because of the break of symmetry, two different classes (A-aad B) of kinks appear and their analytical form is derived. The effect of the adding term is to shrink; a kink A and to widen the neighboring kink B in such a way that the product of their widths keeps constant. Concerning the dynamics, this implies that kinks A move much faster than kinks B. Since the kink profiles approach exponentially the asymptotical values, the time dependence of the average distance L(t)between kinks does not change: L(t)similar to lnt in the absence of noise, and L(t)similar to t(1/3) in the presence of (shot) noise. However, the crossover lime between the first and the second regime may increase even of some orders of magnitude. Finally, our results show that kinks A may be so narrow that their width is comparable to the lattice constant: in this case, they indeed represent a discontinuity of the surface slope, that is, an angular point, and a difference approach to coarsening; should be used.