In this paper we study unique continuation properties of solutions to higher (fifth) order nonlinear dispersive models. The aim is to show that if the difference of two solutions of the equations, u 1 − u 2 , decays sufficiently fast at infinity at two different times, then u 1 ≡ u 2 .

Abstract. We construct a local in time, exponentially decaying solution of the one-dimensional variable coefficient Schrödinger equation by solving a nonstandard boundary value problem. A main ingredient in the proof is a new commutator estimate involving the projections P ± onto the positive and negative frequencies.

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