AI 中文总结
研究具有排斥δ势和局部非均匀系数的一维三次NLS方程，通过构造修正散射映射，证明其能确定δ势强度和非均匀系数，并给出强度的Lipschitz稳定性及系数的Hölder稳定性估计。
AI 中文摘要
我们研究具有排斥δ势和局部非均匀系数的一维三次非线性薛定谔方程。证明了小数据修正散射并构造了相关的向量值修正散射映射，其两个分量编码了由点相互作用引起的频率ξ和-ξ的耦合。表明该映射确定了δ势的强度和非均匀系数。定量地，δ强度以Lipschitz稳定性恢复，而非均匀系数满足Hölder稳定性估计。据我们所知，这些是存在外部势时修正散射映射的首次恢复和稳定性结果。
英文摘要
We study the one-dimensional cubic nonlinear Schrödinger equation with a repulsive delta potential and a localized inhomogeneous coefficient. We prove small-data modified scattering and construct the associated vector-valued modified scattering map, whose two components encode the coupling of the frequencies $ξ$ and $-ξ$ induced by the point interaction. We show that this map determines both the strength of the delta potential and the inhomogeneous coefficient. Quantitatively, the delta strength is recovered with Lipschitz stability, while the inhomogeneous coefficients satisfy a Hölder stability estimate. To our knowledge, these are the first recovery and stability results for a modified scattering map in the presence of an external potential.
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