Orbital stability of KdV multisolitons in $H^{-1}$

Rowan Killip; Monica Visan

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arXiv · 2009.06746

Orbital stability of KdV multisolitons in $H^{-1}$

Rowan Killip·Monica Visan

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Abstract

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 $H^1$.

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Rowan Killip, Monica Visan. 2020-09-14. Orbital stability of KdV multisolitons in $H^{-1}$. https://arxiv.org/abs/2009.06746

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