发表机构
Izmir Institute of Technology; University of Kansas; Bilkent University（伊兹密尔理工学院; 堪萨斯大学; 比尔肯特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对半直线上带负色散系数的高阶非线性薛定谔方程，利用Fokas统一变换结合线性估计，证明其在两类边界条件下的局部适定性，揭示了与正色散情形的关键差异。
AI 中文摘要
我们证明了带有负色散系数的高阶非线性薛定谔方程在非零Dirichlet和Neumann边界数据下的局部Hadamard适定性。该论文揭示了该模型的一个显著特征：与Alkın、Mantzavinos、Ozsari（2024）研究的正色散情形不同，其适定性需要两类边界条件而非一类。这反映了 underlying全局关系的结构限制，该关系最多可消去一个未知边界迹。利用Fokas的统一变换，我们推导了相关受迫线性问题的显式解公式，并建立了半直线上的最优Sobolev和Strichartz估计。这些线性估计结合对应的柯西问题界，在高、低正则性Sobolev空间中均得到局部适定性，以及解映射的局部Lipschitz连续性。
英文摘要
We prove the local Hadamard well-posedness of the higher-order nonlinear Schrödinger equation with negative dispersion coefficient on the half-line under nonzero Dirichlet and Neumann boundary data. The paper uncovers a striking feature of this model: unlike the positive-dispersion case studied in (Alkın, Mantzavinos, Ozsari, 2024), well-posedness requires two boundary conditions rather than one. This reflects a structural limitation in the underlying global relation, which allows elimination of at most one unknown boundary trace. Using the unified transform of Fokas, we derive an explicit solution formula for the associated forced linear problem and establish sharp Sobolev and Strichartz estimates on the half-line. These linear estimates, together with corresponding Cauchy problem bounds, yield local well-posedness in both high- and low-regularity Sobolev spaces, as well as local Lipschitz continuity of the solution map.
Comments15 pages, 2 figures
