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abstract: 'In this paper we consider the Benjamin equation, a partial differential equation that models one-way propagation of long internal waves of small amplitude along the interface of two fluid layers under the effects of gravity and surface tension. We solve the periodic initial-value problem for the Benjamin equation numerically by a new fully discrete hybrid finite-element / spectral scheme, which we first validate by pinning down its accuracy and stability properties. After testing the evolution properties of the scheme in a study of propagation of single - and multi-pulse solitary waves of the Benjamin equation, we use it in an exploratory mode to illuminate phenomena such as overtaking collisions of solitary waves, and the stability of single-, multi-pulse and ‘depression’ solitary waves.'
address:
- 'Mathematics Department, University of Athens, 15784 Zographou, Greece Institute of Applied & Computational Mathematics, FO.R.T.H., 71110 Heraklion, Greece'
- ' Applied Mathematics Department, University of Valladolid, 47011 Valladolid, Spain'
- 'Applied Mathematics Department, University of California, Merced, 5200 North Lake rd. Merced, CA 95343 , USA'
author:
- 'Vassilios A. Dougalis'
- Angel Duran
- Dimitrios Mitsotakis
title: Notes on the numerical solution of the Benjamin equation
---

Introduction
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In this paper we 