2005, 2005(Special): 22-29. doi: 10.3934/proc.2005.2005.22

On a discrete version of the Korteweg-De Vries equation

1. 

University of Cyprus, Department of Mathematics and Statistics, P.O. Box 20537 Nicosia 1678, Cyprus

2. 

Department of Mathematics, College of Charleston, 66 George Street, Charleston, SC 29424-0001, United States

3. 

University of Massachusetts, Lederle Graduate Research Tower, Department of Mathematics and Statistics, Amherst, MA 01003, United States

Received  September 2004 Revised  March 2005 Published  September 2005

In this short communication, we consider a discrete example of how to perform multiple scale expansions and by starting from the discrete nonlinear Schröodinger equation (DNLS) as well as the Ablowitz-Ladik nonlinear Schrödinger equation (AL-NLS), we obtain the corresponding discrete versions of a Korteweg-de Vries (KdV) equation. We analyze in particular the equation obtained from the AL-NLS and discuss its integrability, as well as its connections with previously studied discrete versions of the KdV equation.
Citation: M. Agrotis, S. Lafortune, P.G. Kevrekidis. On a discrete version of the Korteweg-De Vries equation. Conference Publications, 2005, 2005 (Special) : 22-29. doi: 10.3934/proc.2005.2005.22
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