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

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 $t\to +\infty$.

This is the final version. It has appeared in Nonlinear Analysis Volume 274, January 2027, 114253, https://doi.org/10.1016/j.na.2026.114253