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

The Cauchy matrix approach is developed to solve the SU(2)$\mathbf {SU}(2)$ self‐dual Yang–Mills (SDYM) equation. Starting from a Sylvester matrix equation coupled with certain dispersion relations for an infinite number of coordinates, we derive some new relations that give rise to the SDYM equation under Yang's formulation. By imposing further constraints on complex independent variables, a broad class of explicit solutions of the equation under Yang's formulation are obtained.