An introduction to WKB analysis IV

In this talk, we will consider the first Painlevé hierarchy
which is a family of systems that are extensions of
the traditional first Painlevé equation to higher-order ones. We will discuss the construction of formal
solutions with 2m free parameters (instanton-type solutions) for the first Painlevé hierarchy. The main tool for the construction is the multiple-scale analysis.

We remark some problems related our method.
This is a joint work with Takashi Aoki and Naofumi Honda.