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

Wen-Xiu Ma; Benno Fuchssteiner

doi:10.1063/1.532872

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

solv-int 2015-06-26 v2 Exactly Solvable and Integrable Systems

Authors: Wen-Xiu Ma , Benno Fuchssteiner

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Abstract

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.

Keywords

discrete zero curvature equation master symmetry discrete evolution equation nonisospectral flow algebraic structure discrete spectral problem

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@article{arxiv.solv-int/9809009,
  title  = {Algebraic Structure of Discrete Zero Curvature Equations and Master Symmetries of Discrete Evolution Equations},
  author = {Wen-Xiu Ma and Benno Fuchssteiner},
  journal= {arXiv preprint arXiv:solv-int/9809009},
  year   = {2015}
}

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24 pages, LaTex, revised

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

Abstract

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