VARIATIONAL APPROACH TO THE ZAKHAROV-SHABAT SCATTERING PROBLEM

It is shown that the Zakharov-Shabat scattering problem associated with the inverse scattering transform technique for solving the nonlinear Schrodinger equation call be reformulated as a variational problem. This reformulation makes it possible to use direct variational methods for, finding the eigenvalues of the scattering problem, which determines the speed and amplitude of the solitons emerging from a given initial condition. The approach is illustrated by an application to sech-shaped initial conditions.