Zero curvature representation for classical lattice sine-Gordon equation via quantum R-matrix
Abstract
Local M-operators for the classical sine-Gordon model in discrete space-time are constructed by convolution of the quantum trigonometric 4×4 R-matrix with certain vectors in its "quantum" space. Components of the vectors are identified with τ-functions of the model. This construction generalizes the known representation of M-operators in continuous time models in terms of Lax operators and classical r-matrix.
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