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arXiv · 2502.05579

On stabilization at a soliton for generalized Korteweg--De Vries pure power equation for any power $p\in (1,5)$

Scipio Cuccagna·Masaya Maeda
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Abstract

We apply our idea, which previously we used in the analysis of the pure power NLS, consisting in spitting the virial inequality method into a large energy inequality combined with Kato smoothing, to the case of generalized Korteweg--De Vries pure power equations. We assume that a solution remains for all positive times very close to a soliton and then we prove an asymptotic stability result for $t\to +\infty$.

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Scipio Cuccagna, Masaya Maeda. 2025-02-08. On stabilization at a soliton for generalized Korteweg--De Vries pure power equation for any power $p\in (1,5)$. https://arxiv.org/abs/2502.05579

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