Review on long time asymptotics of large data in some nonintegrable dispersive models

Abstract

In this short note we review recent results concerning the long time dynamics of large data solutions to several dispersive models. Starting with the KdV case and ending with the KP models, we review the literature and present new results where virial estimates allow one to prove local energy decay in different regions of space where solitons, lumps or solitary waves are not present.