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The Cauchy matrix approach is developed to solve the SU(2) self-dualYang--Mills equation. Starting from a Sylvester matrix equation coupled withcertain dispersion relation for infinite coordinates, the self-dual Yang--Millsequation under Yang's formulation is constructed. By imposing furtherconstraints on complex independent variables, a broad class of explicitsolutions are obtained.

Cauchy matrix approach to the SU(2) self-dual Yang--Mills equation