Abstract:
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).