English

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

Mathematical Physics 2011-04-26 v1 Symbolic Computation Analysis of PDEs math.MP Exactly Solvable and Integrable Systems

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 {\em Mathematica}. The codes {\sc InvariantsSymmetries.m} and {\sc DDERecursionOperator.m} can aid researchers interested in properties of nonlinear DDEs.

Keywords

Cite

@article{arxiv.1104.4582,
  title  = {Symbolic Computation of Conservation Laws, Generalized Symmetries, and Recursion Operators for Nonlinear Differential-Difference Equations},
  author = {Ünal Göktaş and Willy Hereman},
  journal= {arXiv preprint arXiv:1104.4582},
  year   = {2011}
}

Comments

16 pages, will appear as Chapter 7 in a Springer Book entitled "Nonlinear Systems and Methods For Mechanical, Electrical and Biosystems" with editors: Albert Luo, J.A. Tenreiro Machado and Dumitru Baleanu, expected to be published in 2011