THE NONLINEAR SCHRODINGER HIERARCHY IN PERTURBATION-THEORY

The multiple-scale expansion of a quasi monochromatic wave solution of strongly dispersive and weakly nonlinear wave equations leads, in mos t cases, to the well-known slow amplitude modulation which satisfies t he Nonlinear Schrodinger equation. Here we consider the full expansion , and provide a method of computing higher order effects with the cond ition that the higher coefficients be bounded functions (no secular gr owing in time). The integrability of the NLS equation, and the asympto tic behaviour of its solutions, are the basic ingredients of our const ruction. The present investigation is confined to the continuum spectr um.