On stabilization at a soliton for generalized Korteweg--De Vries pure power equation for any power $p\in (1,5)$
Scipio Cuccagna, Masaya Maeda
公開日: 2025/2/8
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 $t\to +\infty$.