Initial boundary value problem on a half-line for the MKdV equation
  Initial boundary value problem on a half-line for the Modified KdV equation is considered with the boundary conditions equal to zero at the origin and initial condition chosen arbitrary decreasing rapidly enough and this problem is plunged into the scheme of the inverse scattering method. Here the inverse scattering problem is reduced to the Riemann problem on a system of rays on the complex plane. 
I.T.Habibullin