On uniqueness of solution for a nonlinear Schrödinger–Airy equation

We prove that a sufficiently smooth solution to the initial value problem associated to the equation∂tu+iα∂x2u+β∂x3u+iγ|u|2u+δ|u|2∂xu+εu2∂xu¯=0,x,t∈R,is uniquely determined by its values in the semi-line at two different instants of time.