Nn. Huang et al., AN INVERSE SCATTERING TRANSFORM FOR THE MKDV EQUATION WITH NONVANISHING BOUNDARY-VALUE, Journal of mathematical physics, 38(1), 1997, pp. 226-246
The MKdV equation of normal dispersion with non-vanishing boundary val
ue is solved by the inverse scattering transform method. An affine par
ameter is introduced to avoid double-valued functions of the usual spe
ctral parameter. In terms of it the inverse scattering transform is pe
rformed and the inverse scattering equation of Zakharov-Shabat form as
well as of Marchenko form is derived. Dark multi-soliton solutions ar
e 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.