A numerical approach to blow-up issues for dispersive perturbations of Burgers' equation

We provide a detailed numerical study of various issues pertaining to the dynamics of the Burgers' equation perturbed by a weak dispersive term: blow-up in finite time versus global existence, nature of the blow-up, existence for “long” times, and the decomposition of the initial data into solitary waves plus radiation. We numerically construct solitary waves for fractional Korteweg-de Vries equations.