On the persistence properties of solutions of nonlinear dispersive equations in weighted Sobolev spaces

We study persistence properties of solutions to some canonical dispersive models, namely the semi-linear Schr"odinger equation, the $k$-generalized Korteweg-de Vries equation and the Benjamin-Ono equation, in weighted Sobolev spaces $H^s({\mathbb{R}}^n)\cap L^2(\mathrm{\mid }x{\mathrm{\mid }}^{l}dx),s,l>0$