Abstract

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. © 2007 Elsevier Inc. All rights reserved.