A generalization of inverse scattering method

A new scheme of the inverse scattering method is presented by examining a generalized eigenvalue problem of Ablowitz-Kaup-Newell-Segur scheme. As an illustration of novel feature of our scheme, explicit expressions of the eigenvalue problem and the temporal evolution equation of the eigenfunction have been presented for a generalized nonlinear Schroedinger equation, of which nonlinear terms are composed of the usual cubic nonlinear term and the derivative cubic nonlinear term. (author)