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We study persistence properties of solutions to some canonical dispersivemodels, namely the semi-linear Schr\"odinger equation, the $k$-generalizedKorteweg-de Vries equation and the Benjamin-Ono equation, in weighted Sobolevspaces $H^s(\R^n)\cap L^2(|x|^ldx),\;s,\,l>0$

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