  The unified transform method (UTM) for analyzing initial-boundary value (IBV)
problems provides an important generalization of the inverse scattering
transform (IST) method for analyzing initial value problems. In comparison with
the IST, a major difficulty of the implementation of the UTM in general is the
involvement of unknown boundary values. In this paper we analyze the IBV
problem for the massive Thirring model posed in the quarter plane. We show for
this integrable model, the UTM is as effective as the IST method: the
Riemann-Hilbert (RH) problems we formulated for such a problem have explicit
(x,t)-dependence and depend only on the given initial and boundary values; they
do not involve additional unknown boundary values.
