  We address the question of the uniqueness of solution to the initial value
problem associated to the equation \partial_{t}u+i\alpha
\partial^{2}_{x}u+\beta \partial^{3}_{x}u+i\gamma|u|^{2}u+\delta
|u|^{2}\partial_{x}u+\epsilon u^{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.
