  A continuum growth equation in 1+1 dimensions is obtained by considering the
contributions to the underlying current from kinetics of adatoms on the
surface. These considerations reproduce the slope dependent term that
represents a stable or an unstable growth depending on the sign of the
associated coefficient. In addition an h to -h symmetry breaking nonlinear term
is obtained. Implications of this term on stable to unstable transition are
discussed. This term is tilt independent and is expected to be present
independent of the source of the current in the conserved growth. Computer
simulation based on a zero diffusion bias model is used to verify some of the
predictions of the minimal growth equation. It is shown that the growth
equations for cellular automata type models involving instantaneous relaxations
can be obtained from the proposed method by addressing the corresponding
kinetics of adatoms.
