Fourth Painlevé Equation and PT-Symmetric Hamiltonians

This paper is an addendum to earlier papers \cite{R1,R2} in which it was shown that the unstable separatrix solutions for Painlev\'e I and II are determined by PT-symmetric Hamiltonians. In this paper unstable separatrix solutions of the fourth Painlev\'e transcendent are studied numerically and analytically. For a fixed initial value,... Show more