We 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).

JF - arXiv:solv-int/990400 PB - SISSA UR - http://hdl.handle.net/1963/6489 U1 - 6421 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER -