00931nas a2200121   4500008004100000245007500041210006800116260001000184520053900194100002000733700002000753856003600773       2007                        en  d00aOn the reductions and classical solutions of the Schlesinger equations0 areductions and classical solutions of the Schlesinger equations  bSISSA3 aThe Schlesinger equations S(n,m) describe monodromy preserving\\r\\ndeformations of order m Fuchsian systems with n+1 poles. They\\r\\ncan be considered as a family of commuting time-dependent Hamiltonian\\r\\nsystems on the direct product of n copies of m×m matrix algebras\\r\\nequipped with the standard linear Poisson bracket. In this paper we address\\r\\nthe problem of reduction of particular solutions of “more complicated”\\r\\nSchlesinger equations S(n,m) to “simpler” S(n′,m′) having n′ < n\\r\\nor m′ < m.1 aDubrovin, Boris1 aMazzocco, Marta  uhttp://hdl.handle.net/1963/647200981nas 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