MULTI-EXISTENCE OF MULTI-SOLITONS FOR THE SUPERCRITICAL NONLINEAR SCHRODINGER EQUATION IN ONE DIMENSION

For the L-2 supercritical generalized Korteweg-de Vries equation, we proved in [2] the existence and uniqueness of an N-parameter family of N-solitons. Recall that, for any N given solitons, we call N-soliton a solution of the equation which behaves as the sum of these N solitons asymptotically as t -> +infinity. In the present paper, we also construct an N-parameter family of N-solitons for the supercritical nonlinear Schrodinger equation in dimension 1. Nevertheless, we do not obtain any classification result; but recall that, even in subcritical and critical cases, no general uniqueness result has been proved yet.