A COMMENT ON THE INVERSE SCATTERING METHOD FOR SOLVING THE NONLINEAR SCHRODINGER EQUATION

Disregarding that the locations of poles of the transmission coefficient must be in the upper half-plane of k that is given by the usual inverse scattering method, solutions of the nonlinear Schrodinger equation are found from the Gelfand-Levitan-Marchenko equation by taking the poles at arbitrary places in the complex k-plane. By using the technique of matrix calculation, a simple method is given for directly verifying the solutions in satisfying the nonlinear Schrodinger equation. As an example, new solutions corresponding to the locations of two poles in pairs symmetrically about the origin of the complex k-plane is given and its regularity is shown.