We prove that a sufficiently smooth solution to the initial value problem associated to the equation at partial derivative(t)u + i alpha partial derivative(x)(2)u + beta partial derivative(x)(3)u + i gamma vertical bar u vertical bar(2)u + partial derivative vertical bar u vertical bar(2)partial derivative(x)u + epsilon u(x)(2)(u) over bar = 0, x, t epsilon R, is uniquely determined by its values in the semi-line at two different instants of time. (c) 2005 Elsevier Ltd. All rights reserved.641146158