Whitham hierarchy and generalized Picard–Fuchs operators in the $\mathcal N=2$ SUSY Yang–Mills theory for classical gauge groups

We derive infinitely many meromorphic differentials based on the fractional powers of the superpotential arising from hyperelliptic curves. We obtain various differential equations expressed in terms of the moduli derivatives of the Seiberg–Witten differential. Taking advantage of the cross derivatives of these differentials, we can derive some Picard–Fuchs equations and use the Euler operator to obtain a complete set of Picard–Fuchs equations containing the instanton correction term. We solve the complete system of equations by expanding the moduli parameters in power series.