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