  A quasi-microscopic treatment of edge magnetoplasmons (EMP) is presented for
very low temperatures and confining potentials smooth on the scale of the
magnetic length $\ell_{0}$ but sufficiently steep at the edges such that Landau
level (LL) flattening can be discarded. The profile of the unperturbed electron
density is sharp and the dissipation taken into account comes only from
electron intra-edge and intra-LL transitions due to scattering by acoustic
phonons. For wide channels and filling factors $\nu =1$ and 2, there exist
independent EMP modes spatially symmetric and antisymmetric with respect to the
edge. Some of these modes, named edge helicons, can propagate nearly undamped
even when the dissipation is strong. Their density profile changes
qualitatively during propagation and is given by a rotation of a complex vector
function. For $\nu >2,$ the Coulomb coupling between the LLs leads to a
repulsion of the uncoupled fundamental LL modes: the new modes have very
different group velocities and are nearly undamped. The theory accounts well
for the experimentally observed plateau structure of the delay times as well as
for the EMP's period and decay rates.
