Small dispersion limit of the KdV and semiclassical limit of focusing NLS
Seminar Room 1, Newton Institute
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.
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