For the L 2 subcritical and critical (gKdV) equations, Martel [11] proved the existence and uniqueness of multi-solitons. Recall that for any N given solitons, we call multi-soliton a solution of (gKdV) which behaves as the sum of these N solitons asymptotically as t → +∞. More recently, for the L 2 supercritical case, Côte, Martel and Merle [4] proved the existence of at least one multi-soliton. In the present paper, as suggested by a previous work concerning the one soliton case [3], we first construct an N -parameter family of multi-solitons for the supercritical (gKdV) equation, for N arbitrarily given solitons, and then prove that any multi-soliton belongs to this family. In other words, we obtain a complete classification of multi-solitons for (gKdV).

Abstract. We establish the classification of minimal mass blow-up solutions of the L 2 critical inhomogeneous nonlinear Schrödinger equation

Let S be a minimal mass blow up solution of the critical generalized KdV equation as constructed in [25]. We prove both time and space sharp asymptotics for S close to the blow up time. Let Q be the unique ground state of (gKdV), satisfying Q + Q 5 = Q. First, we show that there exist universal smooth profiles Q k ∈ S(R) (with Q0 = Q) and a constant c0 ∈ R such that, fixing the blow up time at t = 0 and appropriate scaling and translation parameters, S satisfies, for any m 0, ∂ m x S(t) −