Spectral Curves and Whitham Equations in Isomonodromic Problems of Schlesinger Type
| dc.creator | Takasaki, Kanehisa | |
| dc.date | 1997-04-08 | |
| dc.date | 1997-11-07 | |
| dc.date.accessioned | 2026-07-07T09:05:17Z | |
| dc.date.available | 2026-07-07T09:05:17Z | |
| dc.description | It has been known since the beginning of this century that isomonodromic problems --- typically the Painlevé transcendents --- in a suitable asymptotic region look like a kind of ``modulation'' of isospectral problem. This connection between isomonodromic and isospectral problems is reconsidered here in the light of recent studies related to the Seiberg-Witten solutions of $N = 2$ supersymmetric gauge theories. A general machinary is illustrated in a typical isomonodromic problem, namely the Schlesinger equation, which is reformulated to include a small parameter $ε$. In the small-$ε$ limit, solutions of this isomonodromic problem are expected to behave as a slowly modulated finite-gap solution of an isospectral problem. The modulation is caused by slow deformations of the spectral curve of the finite-gap solution. A modulation equation of this slow dynamics is derived by a heuristic method. An inverse period map of Seiberg-Witten type turns out to give general solutions of this modulation equation. This construction of general solution also reveals the existence of deformations of Seiberg-Witten type on the same moduli space of spectral curves. A prepotential is also constructed in the same way as the prepotential of the Seiberg-Witten theory. | |
| dc.description | 41 pages, latex, no figures; typos in references are corrected | |
| dc.identifier | https://arxiv.org/abs/solv-int/9704004 | |
| dc.identifier | http://arxiv.org/abs/solv-int/9704004 | |
| dc.identifier | Asian J.Math. 4 (2) (1998), 1049-1078 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149659 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Quantum Algebra | |
| dc.title | Spectral Curves and Whitham Equations in Isomonodromic Problems of Schlesinger Type | |
| dc.type | text |