On uniqueness and decay of solution for Hirota equation

We address the question of the uniqueness of 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,and prove that a certain decay property of the difference u1 − u2 of two solutions u1 and u2 at two different instants of times t = 0 and t = 1, is sufficient to ensure that u1 = u2 for all the time.