论文标题
KDV的有限解决方案：唯一性和几乎周期性的丧失
Bounded solutions of KdV: uniqueness and the loss of almost periodicity
论文作者
论文摘要
我们解决了Korteweg--de Vries（KDV）方程理论中的两个紧迫问题。首先，我们显示了对KDV解决方案的独特性，这些解决方案仅是有限的，没有任何进一步的衰减，规律性，周期性或几乎是周期性假设。 Deift强调的第二个问题是几乎定期的初始数据是否导致了KDV的几乎周期性解决方案。基于新的观察结果，即这对于通风方程是错误的，我们构建了一个几乎周期性的初始数据的示例，其KDV演变保持有限，但在以后几乎无法周期性。我们的独特性结果可确保构建的解决方案是该初始数据的独特开发。
We address two pressing questions in the theory of the Korteweg--de Vries (KdV) equation. First, we show the uniqueness of solutions to KdV that are merely bounded, without any further decay, regularity, periodicity, or almost periodicity assumptions. The second question, emphasized by Deift, regards whether almost periodic initial data leads to almost periodic solutions to KdV. Building on the new observation that this is false for the Airy equation, we construct an example of almost periodic initial data whose KdV evolution remains bounded, but fails to be almost periodic at a later time. Our uniqueness result ensures that the solution constructed is the unique development of this initial data.
