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 ℓ_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 ν

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... =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 ν >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.