Nonlinear differential equations associated with the first Painlevé hierarchy

Abstract

The first Painlevé hierarchy with general solutions in the form of the Painlevé transcendents is considered. The linear system associated with this hierarchy is given. Some new hierarchies with properties similar to the Painlevé hierarchies are presented. It is shown that the solutions of these hierarchies are expressed via the transcendents of the first Painlevé hierarchy. Thus, the list of nonlinear differential equations whose solutions are expressed in terms of non-classical functions is extended.