  In this paper we study the generalized Korteweg de Vries (KdV) equation with
the nonlinear term of order three: $(u^{3+1})_x$. We prove sharp local
well--posedness for the initial and boundary value problem posed on the right
half line. We thus close the gap in the well--posedness theory of the
generalized KdV which remained open after the seminal work of Colliander and
Kenig in \cite{CK}.
