论文标题
$ h^{ - 1} $中KDV Multisolitons的轨道稳定性
Orbital stability of KdV multisolitons in $H^{-1}$
论文作者
论文摘要
我们证明，Korteweg--de Vries方程的多层解决方案在$ H^{ - 1}（\ Mathbb {r}）$中是轨道稳定的。我们介绍了多层的变异表征，在如此低的规律性下仍然有意义，并表明所有优化序列都会收敛到多层的流形。在多层的整个流形中，最初需要的近距离是均匀的。即使以$ h^1 $为单位，此前尚未证明这一点。
We prove that multisoliton solutions of the Korteweg--de Vries equation are orbitally stable in $H^{-1}(\mathbb{R})$. We introduce a variational characterization of multisolitons that remains meaningful at such low regularity and show that all optimizing sequences converge to the manifold of multisolitons. The proximity required at the initial time is uniform across the entire manifold of multisolitons; this had not been demonstrated previously, even in $H^1$.
