Dubrovin, BorisMaltsev, Andrei Ya A2013-02-142013-02-141999-03-30arXiv:solv-int/990400https://openscience.sissa.it/handle/1963/6489We present here the iteration procedure for the determination of free energy ǫ2-expansion using the theory of KdV - type equations. In our approach we use the conservation laws for KdV - type equations depending explicitly on times t1, t2, . . . to find the ǫ2-expansion of u(x, t1, t2, . . .) after the infinite number of shifts of u(x, 0, 0, . . .) ≡ x along t1, t2, . . . in recurrent form. The formulas for the free energy expansion are just obtained then as a result of quite simple integration procedure applied to un(x).enPreprintMAT/07 FISICA MATEMATICA