On the Stokes Geometry of a Unified Family of $P_{\mathrm{J}}$-Hierarchies (J=I, II, IV, 34)

Abstract

The purpose of this paper is to study the Stokes geometry for a unified family of $P_{\mathrm{J}}$-hierarchies (J=I, II, IV, 34) with a large parameter. For a unified family of $P_{\mathrm{J}}$-hierarchies, we give the underlying Lax pair and study the relation between the Stokes geometry of the system of nonlinear ordinary differential equations and that of its underlying Lax pair by using the explicit forms of 0-parameter solutions.