Controllability of the Korteweg–de Vries equation from the right Dirichlet boundary condition

In this paper, we consider the controllability of the Korteweg–de Vries equation in a bounded interval when the control operates via the right Dirichlet boundary condition, while the left Dirichlet and the right Neumann boundary conditions are kept to zero. We prove that the linearized equation is controllable if and only if the length of the spatial domain does not belong to some countable critical set. When the length is not critical, we prove the local exact controllability of the nonlinear equation.