Multivariable Painleve'-II equation: connection formulas for arbitrary system size

Abstract

Connection formulas for the asymptotic solutions of a system of n> 1 coupled Painleve'-II equations with symmetry-breaking parameters are written explicitly. An asymptotically exact WKB approach to these formulas relies on the quantum-mechanical independent crossing approximation for an explicitly time-dependent Schroedinger equation.

45 pages with figures. v3 removed discussion of corrections