Weyl Equation and BPS Monopoles

We apply the ADHMN construction to obtain the SU(n + 1) (for generic values of n) spherically symmetric BPS monopoles with minimal symmetry breaking. In particular, the problem simplifies by solving the Weyl equation, leading to a set of coupled equations, whose solutions are expressed in terms of the Whittaker functions. Next, this construction is generalized for non-commutative SU(n + 1) BPS monopoles, where the corresponding solutions are given in terms of the Heun B functions.