Lagrangian controllability of the Korteweg-de Vries equation with a higher order velocity field for the N-solitons solution

In this article, we study the Lagrangian controllablity of the Korteweg-de Vries (KdV) equation with the higher order velocity field for the N-solitons solution given in [4]. We prove that, for a given depth of the fluid h₀, there exists L_N > 0 such that if L <; L_N, then there exists a time T for which one can transport the fluid located in [0, L] to x > L. Physical applications of this result include the transportation of sediment and of polluted water.