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Symbolic Computation of Conservation Laws, Generalized Symmetries, and Recursion Operators for Nonlinear Differential–Difference Equations

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Dynamical Systems and Methods

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Abstract

Algorithms for the symbolic computation of polynomial conservation laws, generalized symmetries, and recursion operators for systems of nonlinear differential–difference equations (DDEs) are presented. The algorithms can be used to test the complete integrability of nonlinear DDEs. The ubiquitous Toda lattice illustrates the steps of the algorithms, which have been implemented in Mathematica. The codes InvariantsSymmetries.m and DDERecursionOperator.m can aid researchers interested in properties of nonlinear DDEs.

This material is based upon work supported by the National Science Foundation (U.S.A.) under Grant No. CCF-0830783.

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Acknowledgments

J.A. Sanders, J.-P. Wang, M. Hickman, and B. Deconinck are gratefully acknowledged for valuable discussions.

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Authors and Affiliations

  1. Department of Computer Engineering, Turgut Özal University, Keçiören, Ankara, 06010, Turkey

    Ünal Göktaş

  2. Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado, 80401-1887, USA

    Willy Hereman

Authors
  1. Ünal Göktaş
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  2. Willy Hereman
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Corresponding author

Correspondence to Ünal Göktaş .

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Editors and Affiliations

  1. Edwardsville, School of Engineering, Southern Illinois University, Room: EB2064, Edwardsville, 62026-1805, USA

    Albert C.J. Luo

  2. Institute of Engineering, Department of Electrical Engineering, Polytechnic Institute of Porto, Rua Dr António Bernadino Almeida 431, Porto, 4200-072, Portugal

    José António Tenreiro Machado

  3. Faculty of Art and Sciences, Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

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Göktaş, Ü., Hereman, W. (2012). Symbolic Computation of Conservation Laws, Generalized Symmetries, and Recursion Operators for Nonlinear Differential–Difference Equations. In: Luo, A., Machado, J., Baleanu, D. (eds) Dynamical Systems and Methods. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0454-5_7

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  • DOI: https://doi.org/10.1007/978-1-4614-0454-5_7

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-0453-8

  • Online ISBN: 978-1-4614-0454-5

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