%0 Report %D 2007 %T Numerical solution of the small dispersion limit of Korteweg de Vries and Whitham equations %A Tamara Grava %A Christian Klein %X The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\\\\epsilon^2$, is characterized by the appearance of a zone of rapid modulated oscillations of wave-length of order $\\\\epsilon$. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. In this manuscript we give a quantitative analysis of the discrepancy between the numerical solution of the KdV equation in the small dispersion limit and the corresponding approximate solution for values of $\\\\epsilon$ between $10^{-1}$ and $10^{-3}$. The numerical results are compatible with a difference of order $\\\\epsilon$ within the `interior\\\' of the Whitham oscillatory zone, of order $\\\\epsilon^{1/3}$ at the left boundary outside the Whitham zone and of order $\\\\epsilon^{1/2}$ at the right boundary outside the Whitham zone. %B Comm. Pure Appl. Math. 60 (2007) 1623-1664 %G en_US %U http://hdl.handle.net/1963/1788 %1 2756 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-30T13:45:26Z\\nNo. of bitstreams: 1\\n91FM-2005.pdf: 905542 bytes, checksum: 8505fe7c8ac2e5f1da7248d62ae542b2 (MD5) %R 10.1002/cpa.20183