00981nas a2200121   4500008004100000245011300041210007000154260001000224520054300234100002000777700002600797856003600823       1999                        en  d00aRecurrent procedure for the determination of the free energy ε^2 expansion in the topological string theory0 aRecurrent procedure for the determination of the free energy ε2   bSISSA3 a<p>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).</p>1 aDubrovin, Boris1 aMaltsev, Andrei, Ya A  uhttp://hdl.handle.net/1963/6489