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 \partial_{t}u+iα\partial^{2}_{x}u+β \partial^{3}_{x}u+iγ|u|^{2}u+δ|u|^{2}\partial_{x}u+εu^{2}\partial_{x}\bar{u} = 0, \quad x,t \in \R, and prove that a certain decay property of the difference $u_1-u_2$ of two solutions $u_1$ and $u_2$ at two different instants of times $t=0$ and $t=1$, is sufficient to ensure that $u_1=u_2$ for all the time.

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