On a discrete version of the Korteweg-De Vries equation

M. Agrotis; S. Lafortune; P.G. Kevrekidis

doi:10.3934/proc.2005.2005.22

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2005, Volume 2005: 22-29. Doi: 10.3934/proc.2005.2005.22 open access

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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
2.
Department of Mathematics, College of Charleston, 66 George Street, Charleston, SC 29424-0001
3.
University of Massachusetts, Lederle Graduate Research Tower, Department of Mathematics and Statistics, Amherst, MA 01003

Received: August 31, 2004

Revised: February 28, 2005

Published: August 2005

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Abstract

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.

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Mathematics Subject Classification: Primary: 34K99, 35Q53, 35Q55.

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