  For the L^2 subcritical and critical (gKdV) equations, Martel 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 time goes to infinity. More recently, for
the L^2 supercritical case, Cote, Martel and Merle proved the existence of at
least one multi-soliton. In the present paper, as suggested by a previous work
concerning the one soliton case, 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).
