Unique continuation property for a higher order nonlinear Schrödinger equation
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چکیده
We prove that, if a sufficiently smooth solution u to the initial value problem associated with the equation ∂t u+ iα∂2 xu+ β∂3 xu+ iγ |u|2u+ δ|u|∂xu+ u∂xu= 0, x, t ∈R, is supported in a half line at two different instants of time then u≡ 0. To prove this result we derive a new Carleman type estimate by extending the method introduced by Kenig et al. in [Ann. Inst. H. Poincaré Anal. Non Linéaire 19 (2002) 191–208]. 2004 Elsevier Inc. All rights reserved.
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تاریخ انتشار 2005