Internal controllability of non-localized solution for the Kodomtsev-Petviashvili II equation

The internal control problem for the Kadomstev-Petviashvili II equation, known as KP-II, is the object of study in this paper. The controllability in $L^2(T)$ from vertical strip is proved using the Hilbert Unique Method through the techniques of semiclassical and microlocal analysis. Additionally, a negative result for the controllability in $L^2(T)$ from horizontal strip is also showed.