Boundary controllability of a linear Schrödinger-Korteweg-de Vries system

The Schrödinger-Korteweg-de Vries system is a model in fluid mechanics and plasma physics that describes the interactions between a short-wave and a long-wave. This paper is concerned with the null controllability of a linear Schrödinger-Korteweg-de Vries system on a bounded interval, we use two controls acting via the left Dirichlet boundary conditions. First, we prove a Carleman estimate for the adjoint system, then, the null controllability is obtained by duality argument.