  Using recently proposed soliton equations we derive a basic identity for the
scaling violation of $N=2$ supersymmetric gauge theories $\sum_i a_i\partial
F/\partial a_i-2F=8 \pi i b_1 u$. Here $F$ is the prepotential, $a_i$'s are the
expectation values of the scalar fields in the vector multiplet, $u=1/2\, {\rm
Tr}\, \langle\phi^2\rangle$ and $b_1$ is the coefficient of the one-loop
$\beta$-function. This equation holds in the Coulomb branch of all $N=2$
supersymmetric gauge theories coupled with massless matter.
