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Symbolic Computation of Polynomial Conserved Densities, Generalized Symmetries, and Recursion Operators for Nonlinear Differential-Difference Equations

Hereman, W. and Sanders, J. A. and Sayers, J. and Wang, J. P. (2005) Symbolic Computation of Polynomial Conserved Densities, Generalized Symmetries, and Recursion Operators for Nonlinear Differential-Difference Equations. In: Group Theory and Numerical Analysis. CRM Proceedings and Lecture Notes. No.39. American Mathematical Society , Providence, R.I., pp. 133-148. ISBN 0-8218-3565-3 http://resolver.caltech.edu/CaltechAUTHORS:20110818-101146521

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Abstract

Algorithms for the symbolic computation of polynomial conserved densities, fluxes, generalized symmetries, and recursion operators for systems of nonlinear differential-difference equations are presented. In the algorithms we use discrete versions of the Fréchet and variational derivatives, as well as discrete Euler and homotopy operators. The algorithms are illustrated for prototypical nonlinear polynomial lattices, including the Kac-van Moerbeke (Volterra) and Toda lattices. Results are shown for the modified Volterra and Ablowitz-Ladik lattices.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://www.ams.org/bookstore?fn=20&arg1=crmpseries&ikey=CRMP-39PublisherUNSPECIFIED
Additional Information:© 2005 American Mathematical Society. This paper is dedicated to Ryan Sayers (1982-2003). This material is based upon work supported by the National Science Foundation under Grant No. CCR-9901929. M. Hickman and B. Deconinck are gratefully acknowledged for valuable discussions. D. Baldwin is thanked for proof reading the manuscript.
Funders:
Funding AgencyGrant Number
NSFCCR-9901929
Subject Keywords:Homotopy operators, conserved densities, fluxes, recursion operators, complete integrability, differential-difference, DDEs, semi-discrete lattices.
Classification Code:MSC: Primary 37J35, 37K10; Secondary 35Q58, 37K05
Record Number:CaltechAUTHORS:20110818-101146521
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20110818-101146521
Official Citation:W. Hereman, J. A. Sanders, J. Sayers, and J. P. Wang -- Symbolic computation of polynomial conserved densities, generalized symmetries, and recursion operators for nonlinear differential-difference equations
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:24930
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:18 Aug 2011 18:45
Last Modified:26 Dec 2012 13:29

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