  We study the evolution of step bunches on vicinal surfaces using a
thermodynamically consistent step-flow model that (i) circumvents the
quasistatic approximation that prevails in the literature by accounting for the
dynamics of adatom diffusion on terraces and attachment-detachment at steps
(referred to as the dynamical effect), and (ii) generalizes the expression of
the step chemical potential by incorporating the necessary coupling between the
diffusion fields on adjacent terraces (referred to as the chemical effect).
Having previously shown that these effects can explain the onset of step
bunching without recourse to the inverse Ehrlich-Schwoebel (iES) barrier or
other extraneous mechanisms, we are here interested in the evolution of step
bunches beyond the linear-stability regime. In particular, the numerical
resolution of the step-flow problem yields a robust power-law coarsening of the
surface profile, with the bunch height growing in time as $H\sim t^{1/2}$ and
the minimal interstep distance as a function of the number of steps in the
bunch cell obeying $\ell_{min}\sim N^{-2/3}$. Although these exponents have
previously been reported, this is the first time such scaling laws are obtained
in the absence of an iES barrier or adatom electromigration. In order to
validate our simulations, we take the continuum limit of the discrete step-flow
system, leading to a novel nonlinear evolution equation for the surface height.
We investigate the existence of self-similar solutions of this equation and
confirm the 1/2 coarsening exponent obtained numerically for $H$. We highlight
the influence of the combined dynamical-chemical effect and show that it can be
interpreted as an effective iES barrier in the standard BCF theory. Finally, we
use a Pad\'e approximant to derive an analytical expression for the velocity of
steadily moving step bunches and compare it to numerical simulations.
