Symbolic Computation of Recursion Operators for Nonlinear Differential-Difference Equations

Mathematical and Computational Applications

Göktaş, Ünal¹ 

关键词: Conservation Law;    Generalized Symmetry;    Recursion Operator;    Nonlinear Differential-Difference Equation;   

DOI  :  10.3390/mca16010001

学科分类：计算数学

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY