Inverse scattering method for square matrix nonlinear Schr\"odinger   equation under nonvanishing boundary conditions
  Matrix generalization of the inverse scattering method is developed to solve the multicomponent nonlinear Schr\"odinger equation with nonvanishing boundary conditions. It is shown that the initial value problem can be solved exactly. The multi-soliton solution is obtained from the Gel'fand--Levitan--Marchenko equation. 
Jun'ichi Ieda, Masaru Uchiyama, Miki Wadati