We consider the critical Korteweg–de Vries (KdV) equation: \[ u_t + (u_{xx} + u^5)_x=0, \quad t,x \in {\mathbb R}. \] Let $R_j(t,x) = Q_{c_j}(x - x_j - c_jt)$ ( $j = 1, \dots, N$ ) be $N$ soliton solutions to this equation. Denote $U(t)$ the KdV linear group, and let $V \in H^1$ be with sufficient decay on the right; that is, let $(1+x_+^{2+\delta_0}) V \in L^2$ be for some $\delta_0 > 0$ .
¶ We construct a solution $u(t)$ to the critical KdV equation such that \[ \lim_{t \to \infty} \Big\| u(t) - U(t) V - \sum_{j=1}^N R_j (t) \Big\|_{H^1} =0. \]