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For the L2 supercritical generalized Korteweg-de Vries equation, we proved ina previous article the existence and uniqueness of an N-parameter family ofN-solitons. Recall that, for any N given solitons, we call N-soliton a solutionof the equation which behaves as the sum of these N solitons asymptotically astime goes to infinity. In the present paper, we also construct an N-parameterfamily of N-solitons for the supercritical nonlinear Schr\"odinger equation, indimension 1 for the sake of simplicity. Nevertheless, we do not obtain anyclassification result; but recall that, even in subcritical and critical cases,no general uniqueness result has been proved yet.

Multi-existence of multi-solitons for the supercritical nonlinear Schr\"odinger equation in one dimension