  This paper presents an analytical study of the coexistence of different
transport regimes in quasi-one-dimensional surface-disordered waveguides (or
electron conductors). To elucidate main features of surface scattering, the
case of two open modes (channels) is considered in great detail. Main attention
is paid to the transmission in dependence on various parameters of the model
with two types of rough-surface profiles (symmetric and antisymmetric). It is
shown that depending on the symmetry, basic mechanisms of scattering can be
either enhanced or suppressed. As a consequence, different transport regimes
can be realized. Specifically, in the waveguide with symmetric rough
boundaries, there are ballistic, localized and coexistence transport regimes.
In the waveguide with antisymmetric roughness of lateral walls, another regime
of the diffusive transport can arise. Our study allows to reveal the role of
the so-called square-gradient scattering which is typically neglected in
literature, however, can give a strong impact to the transmission.
