论文标题
多层是KDV保守量的独特约束最小化器
Multisolitons are the unique constrained minimizers of the KdV conserved quantities
论文作者
论文摘要
我们考虑以下各种问题：最小化$（n+1）$ st多项式保守数量的kdv kdv，$ h^n（\ mathbb {r}）$，其中第一个$ n $保守的数量约束。 Maddocks和Sachs使用了$ n $ -solitons是此问题的本地最小化器，以证明$ n $ -solitons在$ H^n（\ Mathbb {r}）$中轨道稳定。 给定的$ n $约束可以通过$ n $ -soliton实现，我们表明有一组唯一的$ n $振幅参数，以便相应的多层可以满足约束。此外，我们证明这些多层是独特的全球约束最小化器。然后，我们使用这种变分表征来通过浓度紧凑度提供了Maddock和Sachs轨道稳定性结果的新证明。 如果可以通过$ h^n（\ mathbb {r}）$中的函数获得约束，而不是通过$ n $ - soliton来获得约束时，我们发现了最小化序列的新行为。
We consider the following variational problem: minimize the $(n+1)$st polynomial conserved quantity of KdV over $H^n(\mathbb{R})$ with the first $n$ conserved quantities constrained. Maddocks and Sachs used that $n$-solitons are local minimizers for this problem in order to prove that $n$-solitons are orbitally stable in $H^n(\mathbb{R})$. Given $n$ constraints that are attainable by an $n$-soliton, we show that there is a unique set of $n$ amplitude parameters so that the corresponding multisolitons satisfy the constraints. Moreover, we prove that these multisolitons are the unique global constrained minimizers. We then use this variational characterization to provide a new proof of the orbital stability result of Maddocks and Sachs via concentration compactness. In the case when the constraints can be attained by functions in $H^n(\mathbb{R})$ but not by an $n$-soliton, we discover new behavior for minimizing sequences.
