We study numerically the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\epsilon^{2}u_{xxx}=0$ for $\epsilon\ll1$ and give a quantitative comparison of the numerical solution with various asymptotic formulae for small $\epsilon$ in the whole $(x,t)$-plane. The matching of the asymptotic solutions is studied numerically.
Painleve II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small dispersion limit
Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit
A deformation of the method of characteristics and the Cauchy problem for Hamiltonian PDEs in the small dispersion limit
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