On a discrete version of the Korteweg-De Vries equation

Pages: 22 - 29, Issue Special, August 2005

 Abstract        Full Text (214.3K)              

M. Agrotis - University of Cyprus, Department of Mathematics and Statistics, P.O. Box 20537 Nicosia 1678, Cyprus (email)
S. Lafortune - Department of Mathematics, College of Charleston, 66 George Street, Charleston, SC 29424-0001, United States (email)
P.G. Kevrekidis - University of Massachusetts, Lederle Graduate Research Tower, Department of Mathematics and Statistics, Amherst, MA 01003, United States (email)

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.

Keywords:  Nonlinear SchrÄodinger Equation, Korteweg-de Vries equation, Multiple Scale Expansions, Singularity Confinement.
Mathematics Subject Classification:  Primary: 34K99, 35Q53, 35Q55.

Received: September 2004;      Revised: March 2005;      Published: September 2005.