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Math. Comput. Appl. 2011, 16(1), 1-12; doi:10.3390/mca16010001

Symbolic Computation of Recursion Operators for Nonlinear Differential-Difference Equations

1
Department of Computer Engineering, Turgut Özal University Keçiören, Ankara 06010, Turkey
2
Department of Mathematical and Computer Sciences, Colorado School of Mines Golden, Colorado 80401-1887, USA
*
Author to whom correspondence should be addressed.
Published: 1 April 2011
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Abstract

An algorithm for the symbolic computation of recursion operators for systems of nonlinear differential-difference equations (DDEs) is presented. Recursion operators allow one to generate an infinite sequence of generalized symmetries. The existence of a recursion operator therefore guarantees the complete integrability of the DDE. The algorithm is based in part on the concept of dilation invariance and uses our earlier algorithms for the symbolic computation of conservation laws and generalized symmetries. The algorithm has been applied to a number of well-known DDEs, including the Kacvan Moerbeke (Volterra), Toda, and Ablowitz-Ladik lattices, for which recursion operators are shown. The algorithm has been implemented in Mathematica, a leading computer algebra system. The package DDERecursionOperator.m is briefly discussed.
Keywords: Conservation Law; Generalized Symmetry; Recursion Operator; Nonlinear Differential-Difference Equation Conservation Law; Generalized Symmetry; Recursion Operator; Nonlinear Differential-Difference Equation
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Göktaş, Ü.; Hereman, W. Symbolic Computation of Recursion Operators for Nonlinear Differential-Difference Equations. Math. Comput. Appl. 2011, 16, 1-12.

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Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
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