### Abstract

We compare numerically the small dispersion limit of the Korteweg de Vries equation with the asymptotic formulas obtained in the works of Lax-Levermore and Deif-Venakides and Zhou. We compare numerically the semiclassical limit of the focusing nonlinear Schrodinger equation with the asymptotic formula obtained in the works of Kamvissis-McLaughlin-Miller and Tovbis-Venakides-Zhou. As a results we outline the regions of the (x,t) where the above asymptotic formulas give a satisfactory description of the respective equations.