A numerical study of the small dispersion limit of the Korteweg–de Vries equation and asymptotic solutions

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 << 1 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