On the configuration of classical Yang-Mills fields with topological charge $k=4$

The solutions of the nonlinear matrix equation in the Atiyah-Hitchin-Drifeld-Manin (AHDM) construction that determine the Yang-Mills self-dual fields with topological charge ${k=4}$ for symplectic gauge groups are discussed. In the case of $\textrm{Sp}(n)$, ${n>2}$, it is possible to use a procedure that was proposed earlier for generating solutions with ${k=3}$. It is shown that for $SU(2)=\textrm{Sp}(1)$) the AHDM matrix can be generated by using cubic equation solutions with coefficients that depend on ${8k-3}$ parameters.