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We study the boundary,controllability of a nonlinear Korteweg-de Vries equation with the Dirichlet boundary condition on an interval with a critical length for which it has been shown by Rosier that the linearized control system around the origin is not controllable. We prove that the nonlinear term gives the local controllability around the origin Key-words: Exact boundary controllability, Korteweg-de Vries, nonlinear equation, missed directions  Université de Paris-Sud Laboratoire ANEDP, Mathématique, UMR 8628, Bât. 425, 91405 Orsay cedex, France

Exact boundary controllability of a nonlinear KdV equation with critical lengths