On stabilization at a soliton for generalized Korteweg–De Vries pure power equation for any power p ∈ (1, 5)

We apply our idea, which we previously used in the analysis of the pure power NLS, consisting of splitting 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 → +∞