Unique continuation properties of the higher order nonlinear Schrödinger equations in one dimension

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• 作者：Zhiwen Duan ^{duanzhw@hust.edu.cn} ; Quan Zheng
• 关键词：Higher order Schr&ouml ; dinger equation ; Carleman estimate ; Unique continuation
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 May 2017
• 年：2017
• 卷：449
• 期：2
• 页码：941-965
• 全文大小：430 K
• 卷排序：449

文摘

In this paper, we study the unique continuation properties of the higher order nonlinear Schrödinger equations in one dimension and show exponential decay weighted estimates, as well as a LpLp-type Carleman estimate based on the Littlewood–Paley theory. As a consequence we obtain that if u   is a solution of the Schrödinger equation such that there exists X0≠±∞X0≠±∞ with suppu(⋅,0)suppu(⋅,0), suppu(⋅,1)⊆(−∞,X0)suppu(⋅,1)⊆(−∞,X0) (or (X0,+∞)(X0,+∞)) then u≡0u≡0 in R×[0,1]R×[0,1].