The Korteweg–de Vries–Kawahara equation in a bounded domain and some numerical results

We are concerned with the initial-boundary problem associated to the Korteweg–de Vries–Kawahara perturbed by a dispersive term which appears in several fluids dynamics problems. We obtain local smoothing effects that are uniform with respect to the size of the interval. We also propose a simple finite different scheme for the problem and prove its unconditional stability. Finally we give some numerical examples.