Monodromy deformation approach to the scaling limit of the Painleve first equation

Abstract

The isomonodromy deformation equation for a 2x2 matrix linear ODE with a large parameter can be locally reduced to a (hyper)elliptic equation. To globalize this result, we apply the isomonodromy deformation method and obtain the modulation equations for the asymptotic algebraic curve. The method is applied to the degenerate solution of the Painleve first equation.

arXiv comment24 pages, LaTeX; additional references, example and comments are included

References in corpus (2)

• Non-linear WKB Analysis of the String Equation
• Nonlinear Quasiclassics and the Painlevé Equations

Cited by in corpus (5)

• Quasi-linear Stokes phenomenon for the Painlevé first equation
• Viscous shocks in Hele-Shaw flow and Stokes phenomena of the Painleve I transcendent
• Shocks and finite-time singularities in Hele-Shaw flow
• On an isomonodromy deformation equation without the Painlevé property
• On the tritronquée solutions of P${}_I^2$