Extended double soliton solution families for the statically axisymmetric self-dualSU(2) gauge field equations

By using the extended double complex function method, the statically axisymmetric self-dualSU(2) gauge field equations and, in turn, the Belinsky-Zakharov solution-generating technique are generalized to extended double forms. The restriction on “soliton index” in the original solution-generating technique is eliminated so that for each positive integer, we can obtainphysical soliton solutions of the statically axisymmetric self-dualSU(2) gauge field equations in pairs. Some sufficient conditions are given for seed solutions with which the corresponding scattering wave function can be written out directly. As examples, some soliton solution families are given, most solutions of which are new.