Recurrent procedure for the determination of the Free Energy $\epsilon^{2}$expansion in the Topological String Theory
Abstract
We present here the iteration procedure for the determination of free energy $\epsilon^{2}$expansion using the theory of KdV  type equations. In our approach we use the conservation laws for KdV  type equations depending explicitly on times $t_{1}, t_{2}, ...$ to find the $\epsilon^{2}$expansion of $u(x,t_{1},t_{2},...)$ after the infinite number of shifts of $u(x,0,0,...) \equiv x$ along $t_{1}, t_{2}, ...$ in recurrent form. The formulas for the free energy expansion are just obtained then as a result of quite simple integration procedure applied to $u_{n}(x)$.
 Publication:

arXiv eprints
 Pub Date:
 March 1999
 DOI:
 10.48550/arXiv.solvint/9904004
 arXiv:
 arXiv:solvint/9904004
 Bibcode:
 1999solv.int..4004D
 Keywords:

 Exactly Solvable and Integrable Systems;
 High Energy Physics  Theory;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 18 pages, Latex