TY - JOUR T1 - Numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions JF - Physica D 241, nr. 23-24 (2012): 2246-2264 Y1 - 2012 A1 - Tamara Grava A1 - Christian Klein KW - Korteweg-de Vries equation AB - 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. PB - Elsevier U1 - 7069 U2 - Physics U4 - -1 ER -