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∂xū=0,x,t∈R,is uniquely determined by its values in the semi-line at two different instants of time. © 2005 Elsevier Ltd. All rights reserved.641146158Bourgain, J., On the compactness of the support of solutions of dispersive equations (1997) Int. Math. Res. Notices, 9, pp. 437-447Carvajal, X., (2002), Ph.D. Thesis, IMPA, Rio de Janeiro, BrazilCarvajal, X., Linares, F., (2003) Some Properties for a Higher Order Nonlinear Schrödinger Equation, , PreprintCarvajal, X., Linares, F., A higher order nonlinear Schrödinger equation with variable coefficients (2003) Diff. Int. Equations, 16, pp. 1111-1130Carvajal, X., Panthee, M., Unique continuation property for a higher order nonlinear Schrödinger equation (2005) J. Math. Anal. Appl., 303 (1), pp. 188-207Hasegawa, A., Kodama, Y., Nonlinear pulse propagation in a monomode dielectric guide (1987) IEEE J. Quantum Electron., 23 (5), pp. 510-524Iório Jr., R.J., (2001) Unique Continuation Principles for the Benzamin-Ono Equation, , Preprint, IMPAIório Jr., R.J., (2002) Unique Continuation Principles for Some Equations of Benzamin-Ono Type, , Preprint, IMPAIsakov, V., Carleman type estimates in an anisotropic case and applications (1993) J. Diff. Equations, 105, pp. 217-238Kenig, C.E., Ponce, G., Vega, L., On the support of solutions to the generalized KdV equation (2002) Ann. Inst. H. Poincaré Anal. Non Linéaire, 19 (2), pp. 191-208Kenig, C.E., Ponce, G., Vega, L., On the unique continuation of solutions to the generalized KdV equation (2003) Math. Res. Lett., 10 (5-6), pp. 833-846Kenig, C.E., Ponce, G., Vega, L., On unique continuation for nonlinear Schrödinger equation (2003) Commun. Pure Appl. Math., 56, pp. 1247-1262Kenig, C.E., Ruiz, A., Sogge, C., Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators (1987) Duke Math. J., 55, pp. 329-347Kodama, Y., Optical solitons in a monomode fiber (1985) J. Statist. Phys., 39 (56), pp. 597-614Laurey, C., The Cauchy problem for a third order nonlinear Schrödinger equation (1997) Nonlinear Anal.Theory, Methods and Appl., 29, pp. 121-158Mizohata, S., Unicité du prolongement des solutions pour quelques operateurs differentials paraboliques (1958) Mem. Coll. Sci. Univ. Kyoto, 31, pp. 219-239Panthee, M., A note on the unique continuation property for Zakharov-Kuznetsov equation (2004) Nonlinear Anal.Theory, Methods and Appl., 59 (3), pp. 425-438Panthee, M., Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation (2005) Electron. J. Diff. Equations, 2005 (59), pp. 1-12Saut, J.C., Scheurer, B., Unique continuation for some evolution equations (1987) J. Diff. Equations, 66, pp. 118-139Staffilani, G., On the generalized Korteweg-de Vries-type equations (1997) Diff. Int. Equations, 10 (4), pp. 777-796Tataru, D., Carleman type estimates and unique continuation for the Schrödinger equation (1995) Diff. Int. Equations, 8 (4), pp. 901-905Zhang, B., Unique continuation for the Korteweg-de Vries equation (1992) SIAM J. Math. Anal., 23, pp. 55-71