  We investigate the type IIA AdS(3) x S(3) x M(4) superstring with M(4)=S(3) x
S(1) or M(4)=T(4). String theory in this background is interesting because of
AdS3/CFT2 and its newly discovered integrable structures. We derive the kappa
symmetry gauge-fixed Green-Schwarz string action to quadratic order in fermions
and quartic order in fields utilizing a near BMN expansion. As a first
consistency check of our results we show that the two point functions are
one-loop finite in dimensional regularization. We then perform a Hamiltonian
analysis where we compare the energy of string states with the predictions of a
set of conjectured Bethe equations. While we find perfect agreement for single
rank one sectors, we find that the product SU(2) x SU(2) sector does not match
unless the Bethe equations decouple completely. We then calculate 2 to 2
bosonic tree-level scattering processes on the string worldsheet and show that
the two-dimensional S-matrix is reflectionless. This might be important due to
the presence of massless worldsheet excitations which are generally not
described by the Bethe equations.
