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We study the fully discrete elliptic integrable model Q4 and its immediate trigonometric and rational counterparts (Q3, Q2, and Q1). Singular boundary problems for these equations are systematized in the framework of global singularity analysis. We introduce a technique to obtain solutions of such problems, in particular, constructing the exact solution on a regular singularity-bounded strip. The ...

Singular-Boundary Reductions of Type-Q ABS Equations