%0 Report %D 1999 %T Recurrent procedure for the determination of the free energy ε^2 expansion in the topological string theory %A Boris Dubrovin %A Andrei Ya A Maltsev %X

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).

%B arXiv:solv-int/990400 %I SISSA %G en %U http://hdl.handle.net/1963/6489 %1 6421 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:03:06Z No. of bitstreams: 1 dubrovin_maltsev_1999.pdf: 156918 bytes, checksum: b8e98c45d6ed83c8762446339a79418a (MD5)