1202.0962 (T. Grava et al.)

Numerical study of the small dispersion limit of the Korteweg-de Vries
equation and asymptotic solutions    [PDF]

T. Grava, C. Klein

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.

View original: http://arxiv.org/abs/1202.0962