Algebraic Structure of Discrete Zero Curvature Equations and Master Symmetries of Discrete Evolution Equations

Details Algebraic Structure of Discrete Zero Curvature Equations and Master Symmetries of Discrete Evolution Equations Algebraic Structure of Discrete Zero Curvature Equations and Master Symmetries of Discrete Evolution Equations

1998-09-03

arxiv.org/abs/solv-int/9809009v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

24 pages, LaTex, revised

Scientific paper

An algebraic structure related to discrete zero curvature equations is established. It is used to give an approach for generating master symmetries of first degree for systems of discrete evolution equations and an answer to why there exist such master symmetries. The key of the theory is to generate nonisospectral flows $(\lambda_t=\lambda ^l, l\ge0)$ from the discrete spectral problem associated with a given system of discrete evolution equations. Three examples are given.

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