An inverse scattering transform for the MKdV equation with non-vanishing boundary value

The MKdV equation of normal dispersion with non-vanishing boundary value is solved by the inverse scattering transform method. An affine parameter is introduced to avoid double-valued functions of the usual spectral parameter. In terms of it the inverse scattering transform is performed and the inverse scattering equation of Zakharov-Shabat form as well as of Marchenko form is derived. Dark multi-soliton solutions are found formally by means of the Binet-Cauchy formula. The asymptotic behaviors in the Limits of \t\-->infinity are derived as expected. (C) 1997 American Institute of Physics.