Abstract: The unique continuation property is one of the important properties of the solutions to the integrable systems. The properties of the solutions of the initial value problems are bound up with the smoothness of the initial values. In this paper, we mainly discuss the unique continuation property of the solutions to the initial value problem associated with a class of fifth-order KdV equations. We prove that, if a sufficiently smooth solution to the initial value problem associated with the fifth-order Korteweg-de-Vries equations is supported compactly in a nontrivial time interval, then it vanishes identically.

Key words: a class of fifth-order Korteweg-de-Vries equations, compact support, unique continuation property