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:
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arXiv e-prints
- Pub Date:
- March 1999
- DOI:
- 10.48550/arXiv.solv-int/9904004
- arXiv:
- arXiv:solv-int/9904004
- Bibcode:
- 1999solv.int..4004D
- Keywords:
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- Exactly Solvable and Integrable Systems;
- High Energy Physics - Theory;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 18 pages, Latex