The Korteweg-de Vries-Kawahara equation in a bounded domain and some numerical results (Q2383825)

Initial boundary value problems for the Korteweg-de Vries-Kawahara (KdVK) equation perturbed by a dispersive term are considered. It is shown that the KdVK equation has smoothing effects with respect to the size of the interval. A simple finite difference scheme is proposed which is shown to be unconditionally stable. Numerical results are also presented for the interaction of two solitons and a comparison with an analytic solution is given. As main result a local existence and uniqueness theorem is proven.