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).

}, url = {http://hdl.handle.net/1963/6489}, author = {Boris Dubrovin and Andrei Ya A Maltsev} }