Controllability of quasi-linear Hamiltonian NLS equations
  We prove internal controllability in arbitrary time, for small data, for quasi-linear Hamiltonian NLS equations on the circle. We use a procedure of reduction to constant coefficients up to order zero and HUM method to prove the controllability of the linearized problem. Then we apply a Nash-Moser-H\"ormander implicit function theorem as a black box. 
Pietro Baldi, Emanuele Haus, Riccardo Montalto
math.AP