Boundary controllability for the non linear Korteweg-de Vries equation on any critical domain, preprint 2007

Abstract. We consider the boundary controllability problem for a nonlinear Korteweg–de Vries equation with the Dirichlet boundary condition. We study this problem for a spatial domain with a critical length for which the linearized control system is not controllable. In order to deal with the nonlinearity, we use a power series expansion of second order. We prove that the nonlinear term gives the local exact controllability around the origin provided that the time of control is large enough