The virial--Kato method and the asymptotic stability of solitons of the generalized Benjamin, Bona and Mahony equation

Abstract

We apply to the generalized pure power Benjamin, Bona and Mahony equation our method of combining high energy virial estimates with Kato smoothing, which closes the virial estimates in a natural way and allows us to prove a result of asymptotic stability for all the stable solitons with $c>1$ for all the exponents $p>1$.