@article {2012, title = {Numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions}, journal = {Physica D 241, nr. 23-24 (2012): 2246-2264}, number = {arXiv:1202.0962;}, year = {2012}, publisher = {Elsevier}, abstract = {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.}, keywords = {Korteweg-de Vries equation}, doi = {10.1016/j.physd.2012.04.001}, author = {Tamara Grava and Christian Klein} }