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Using recently proposed soliton equations we derive a basic identity for thescaling violation of $N=2$ supersymmetric gauge theories $\sum_i a_i\partialF/\partial a_i-2F=8 \pi i b_1 u$. Here $F$ is the prepotential, $a_i$'s are theexpectation values of the scalar fields in the vector multiplet, $u=1/2\, {\rmTr}\, \langle\phi^2\rangle$ 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.Comment: 10 pages, latex, no figures, a reference adde

PREPOTENTIALS OF N=2 SUPERSYMMETRIC GAUGE THEORIES AND SOLITON EQUATIONS