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On the basis of loop group decompositions (Birkhoff decompositions), we givea discrete version of the nonlinear d'Alembert formula, a method of separationof variables of difference equations, for discrete constant negative Gausscurvature (pseudospherical) surfaces in Euclidean three space. We also computetwo examples by this formula in detail.

Nonlinear d'Alembert formula for discrete pseudospherical surfaces