On uniqueness properties of solutions of the Zakharov-Kuznetsov equation

We prove that if the difference of two sufficiently smooth solutions of the Zakharov-Kuznetsov equation∂tu+∂x3u+∂x∂y2u+u∂xu=0,(x,y)∈R2,t∈[0,1], decays as e−a(x2+y2)3/4 at two different times, for some a>0 large enough, then both solutions coincide.