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

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 $({\lambda }_t={\lambda }^l,l\ge 0)$ from the discrete spectral problem associated with a given system of discrete evolution equations. Three examples are given.

24 pages, LaTex, revised

References in corpus (4)

• A discrete time relativistic Toda lattice
• Discrete time Bogoyavlensky lattices
• An Approach to Master Symmetries of Lattice Equations
• Lax Representations and Zero Curvature Representations by Kronecker Product

Cited by in corpus (12)

• Semi-direct sums of Lie algebras and discrete integrable couplings
• A discrete variational identity on semi-direct sums of Lie algebras
• Continuous Symmetries of Difference Equations
• New symmetries for the Ablowitz-Ladik hierarchies
• Integrable properties of the differential-difference Kadomtsev-Petviashvili hierarchy and continuum limits
• Non-commutative lattice modified Gel'fand-Dikii systems
• Symmetry algebra of discrete KdV equations and corresponding differential-difference equations of Volterra type
• Symmetries and Lie algebra of the differential-difference Kadomstev-Petviashvili hierarchy
• Non-isospectral extension of the Volterra lattice hierarchy, and Hankel determinants
• Higher Order Potential Expansion for the Continuous Limits of the Toda Hierarchy
• Symmetries for the Ablowitz-Ladik hierarchy: I. Four-potential case
• Conservation laws by symmetries and adjoint symmetries