Out-of-equilibrium step meandering on a vicinal surface

A theory of step meandering on a vicinal surface is developed. At equilibrium, the meander w similar to [ln(L)](1/2), where L is the lateral extent. During step flow growth, the diffusive repulsion prevails over elasticity. It leads to new scaling laws for the meander w as a function of the interstep distance I, etc. For a weak Schwoebel effect, we find w similar to l(1/4) (at equilibrium w similar to I). The diffusive repulsion behaves as l lnl. Dynamics tend to ''cure'' meandering. At higher growth speed, deterministic roughening intervenes. In this regime we derive general nonlinear equations for interacting ''lines.'' Disordered structures seem to prevail.