On Solution of the Integrable Initial Boundary Value Problem for KdV Equation on the Semi-axis

This paper is concerned with the Korteweg-de Vries (KdV) equation on the right semi-axis. The initial boundary value problem with inhomogeneous integrable boundary conditions is studied. We show that, under some conditions on the initial data the problem has a solution and provide the procedure for constructing this solution. The procedure is based on the inverse spectral method and consists of several steps reducing to either solving some linear problems or calculations via some explicit formulas.