Generalized inverse scattering transform for the nonlinear Schrodinger equation for bound states with higher multiplicities

We consider a generalization of the inverse scattering transform for the nonlinear Schrodinger (NLS) equation when bound states have multiplicities greater than one. This generalization is accomplished by deriving an explicit compact formula for the time evolution of the norming constants in the presence of nonsimple bound states. Such a formula helps to find explicit solutions to the NLS equation and obtain a generalization of soliton solutions.