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

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

2011-04-23

arxiv.org/abs/1104.4582v1

Physics

Mathematical Physics

16 pages, will appear as Chapter 7 in a Springer Book entitled "Nonlinear Systems and Methods For Mechanical, Electrical and B

Scientific paper

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.

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